History: Fiction or Science? (Chronology, No. 1)

Book Description

Recorded history is a finely-woven magic fabric of intricate lies about events predating the sixteenth century. There is not a single piece of evidence that can be reliably and independently traced back earlier than the eleventh century. This book details events that are substantiated by hard facts and logic, and validated by new astronomical research and statistical analysis of ancient sources.

Customer Reviews:

Calculations are only as good as your numbers.......2007-08-03

Yes, we can all agree that mainstream history is nearly 100% BS due to politics, economics, ego, problems with dating techniques, and various conspiracies. Agreed. But, I've been researching the distinct possibility that human history (in terms of civilizations) are much more ancient than we've been told, so coming across this book was very interesting to me. I wondered how Fomenko could be wrong (if at all) because he is very persuasive in his presentations. Then it dawned on me. If at previous times in prehistory, due to the various catastrophies that are well documented (comets, asteroids, planetary disruptions, plasma discharge, pole reversals, etc) the Earth was in a different position in relation to the sun, different tilt on its axis, different orbit, different rotation (in terms of velocity and DIRECTION), and the continents were in different positions, then would this not cause the ancients to see the sky (constellations) differently? In other words, is Fomenko making erronious assumptions about the physics of the Earth in pre-history, which then corrupt his data with regards to dating the relevant astrology? The last event to seriously disrupt our planet occured roughly 3500 years ago, according to other good researchers, so is it possible Fomenko has been confused by this? The vastly different physics of our planet in the not so distant past may explain this confusion, which is not to say the "mainstream" version of history is correct; on the contrary. I am not an expert in these fields, but wanted to see if this idea could spark discussion.

Pants on fire?.......2007-07-19

Will people ever read before spamming? Yes, Jesuits could not rewrite world history alone, they had help. Anyway, Dr Prof Acad A.Fomenko does not point to jesuits as the driving force of world wide history manipulation in published volumes 1,2,3;, actually he barely mentions the poor devils. Check it with 'Search inside' feature, please. China is rarely mentioned either, in fact, Dr Fomenko is completely eurocentric. Right, his theory contradicts all mainstream schools of history, because in their actual state they are all built on blatantly erroneus chronology. You don't need a mysterious cabal (conspiracy) to falsify history, the falsification is its modus operandi. It is inherent to history(ians) to falsify (distort) events, as it is inherent to humans to boast as it is inherent to power (authority) to legimize itself by referrring to glorious past made to its own order. Dr Prof Fomenko and team have identified scores of instances of such manipulation in Russian, European, etc.. history, and delivered valid statistical proof thereof. His own 'reconstruction' is completely another story. Forget c14 as a valid method of dating. W.Libby has initially discovered a brilliant method of INDEPENDENT dating. Too bad, c14 method has become a joke after a forced marrige with dendrochronology with consensual chronological scale inbuilt. Radiocarbon method can't stand blind tests, but is so very productive as a rubberstamp.

Accepted History & Chronology Must Be Changed. .......2007-04-09

There is no doubt that history as most know it is a sham, & institution's version of History both University & Church is fradulent & inaccurate. Everything was established with an agenda, The real "Dark Ages" are now when we have access to incredible amounts of information past authorities & more important 'common folk' didn't have but our institutions & educators are slow to evolve because of what has ignorantly & arrogantly been taught for too long. This is on many subjects not just Chronology.

For anyone to question "Why would a Mathematician have anything credible to say of History?" The answer is from Dr. Fomenko's preface in the book: "It would be worthwhile to remind the reader that in the XVI-XVII century Chronology was considered to be a subdivision of Mathematics." These volumes could possibly be some of the most important works to date & should be read by everyone with an interest in History, especially professors & educators who have a duty to the public. I have read both books & must say that 'Chronology 1' has some very eye opening & revolutionary information. Even if these volumes are part true the implications are profound & opens the doors to further investigations & questions which must be done. I speak several different lanquages & must say the logic Dr. Fomenko uses with "inflection" of words & words being read from left to right in one region & right to left in another then written backwards, the removal of vowels & get down to basics of words, or different cities & locations having the same name etc. is correct. Vowel usage has always been optional & varied, actually complicating linquistics & study. The first thing one has to understand is that words never had a fixed spelling in history like we do now, the spelling of words was mutable & regional, as well as names & titles of people were vast, varied & changed, NOTHING WAS FIXED or understood linear. Matters of Life & Death as well as financial profiteering yesterday & today were & are made with ignorant, illogical & conspiratorial views of history & reality, it's time people get closer to the Truth & society collectively grow up.

Very Interesting.......2007-03-07

It is a good proposal and I believe it will mature into something even better in the future. I think it deserves to be read.

History as Science Fiction.......2007-01-10

Anatoly Fomenko has written a very intriguing book, full of pictures, charts, and computer 'proof' of his thesis: backwards of AD900 we don't really know what happened or when. Between AD900 and AD1600 there is more certainty, but there is still a lot of fuzzy ground, and things don't get reliable until we get past the 1600's where the printing press made it very difficult for the perpetrators of this timeline manipulation to change anything that had been committed to print. The Dark Ages did not happen. Books were burned for a reason. One organization has doubled the actual length of its existence by expanding the real chronology. Read why.

I had always wondered why Christ died about AD33 and yet men waited until the 11th century to form the Knights Templar, the Cathars, etc and go after the Holy Land by force. Why the 1000 year gap? Turns out there wasn't more than a 10-12 year gap and he proves it using astronomy. This also implies that the planet is not as old as we have been told, and current Christian and other creationist scientists are already championing that idea without being aware of Fomenko's book. The two groups, creationist scientists and the Russian mathematical analysts corroborate each other. Fascinating.

Of course, all this flies in the face of what we have been told traditionally is the 'proper' chronology of western civilization, and most readers will experience 'cognitive dissonance' in reading this book. It means that our history going backwards from AD1600 becomes progressively more incorrect and unreliable until it cannot be trusted at all... in the space of 700-800 years.

Naturally, the curious, open-minded reader will want to know WHO did this, WHY, and did any of the events we think of as really ancient ever happen?
Dr. Fomenko is a respected scientist/mathematician at Moscow State University who has already answered these questions to the satisfaction of his initially skeptical colleagues. Most of them are now believers, a few still refuse to believe (the usual diehards), and of course the western press has ignored Fomenko's work -- for obvious reasons when you read the book. The ones who perpetrated this chronology ruse have a lot to answer for. They are still with us. That's why this book is a well-kept secret.

I gave the book a 4-star rating because I was unable to check out some of his claims; those I checked were as he said. But if even 1/3 of his claims are true, this punches a big hole in what we think is our history, the meaning of western civilization, our educational process (for repeating the ruse as gospel), and the trustworthiness of the organization that perpetrated this ruse, well-intentioned or not.

This book relates to current research into a Young Earth paradigm, to John Keel's discoveries about our planet, and Fr Malachi Martin's insights (in his now out-of-print books). We are indeed sheep who are manipulated and kept ignorant -- for a reason. While knowing what these men have to say may be the "booby prize" (as in: 'what can you do with this knowledge?'), it will provide interesting reading. Didn't someone say: "...and the Truth will set you free."?? For you to judge if this book contains the truth.

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All in one place
The Single Best Reference on the Roman Army!
Complete coverage
Detailed guide to Roman Army operations
Worth the money

The Complete Roman Army
Adrian Goldsworthy
Manufacturer: Thames & Hudson
ProductGroup: Book
Binding: Hardcover

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ASIN: 0500051240

Book Description

The Roman army was one of the most successful fighting forces in history. Its highly advanced organization and tactics were unequaled until the modern era, and monuments to its perseverance and engineering skill are still visible today throughout Europe and the Mediterranean world.

This book is the first to examine in detail not just the early imperial army, but also the citizens' militia of the republic and the army of the later empire. Every aspect of the Roman army, from the daily lives of individual soldiers to the outcome of major campaigns, is explored:

• The Republican Army considers the earliest armies, the creation of the Roman navy, and the militia army that conquered the Mediterranean.
• The Professional Army describes reforms under Marius and his successors and the creation of the new legionary structure.
• The Life of a Roman Soldier looks in detail at all aspects, from recruitment and daily routine to equipment and off-duty life.
• The Army at War reveals how the army operated, from grand tactics to hand-to-hand combat and siege warfare.
• The Army of Late Antiquity examines the reorganization after the defeats of the third century and the rise in the use of cavalry.

Discussions of key Roman battles and brief biographies of the great commanders bring the army's campaigns and personalities to life, while hundreds of photographs, diagrams, and specially commissioned battle plans illustrate the many aspects of the Roman army over several centuries. 245 illustrations, 107 in color.

Customer Reviews:

All in one place.......2007-09-01

Because I am writing a novel about the Roman Army I was looking for a source that brings my research together. Having read several of Goldworthy's works I knew this book would be well researched and very readable. I was not disappointed. The graphics are great, drawings, paintings, maps, diagrams and photos really bring support the text and answer a lot of questions that even a professional researcher may have.

The complete Roman Army is just that. Although it will not stand alone, it is the one work I have in my library that answers the lions share of my questions. Since buying my first copy nearly two years ago, I have begun sending it as a gift item to other enthusiasts, even one to my editor. This book is a good investment.

The Single Best Reference on the Roman Army!.......2007-06-30

If you are going to buy one book on the Roman Army - this should be that book!

Historian Adrian Goldsworthy write authoratively and in great detail on every aspect of the Roman Army, including the Republican Army, the Professional Army, the life of the Roman soldier, the Roman Army at war, and the Army of late Antiquity.

This book, which is a great read and is lavishly illustrated with maps, photographs, timelines and charts, provides unparalleled insight into the armies of the Caesar's as well as all aspects of warfare through the late 3rd Century.

Complete coverage.......2007-04-30

Adrian Goldworthy's The Complete Roman Army gives a pretty complete coverage of the Roman legions during their heydays during the late Republican and early Imperial periods. It reflects on the gradual evolution of the Roman army as it developed from a semi-professional civilian army of the Senate to a permanent professional forces under the Caesars.

The book gives a pretty complete coverage of this army. The information given is clear and written with clarity. There's enough to provide the needed information and no more. It refreshing that there is no overkill of information that will only result in clutter for a book like this. The balance of the information given is just right. The book comes loaded with well drawn illustrations, nice photos, maps and diagrams that gives a clear and understandable images to accompanied the text. As one previous reviewer wrote, it truly is one of the best single volume reference book on the Roman legions during its heydays.

And that is what this book is, a reference guide to the Roman legions. Anyone seeking a quick answer to any questions on the Roman legions, this is the book to touch on. I have loan out this book to people who are not historically minded but like to read Roman historical fictions like Simon Scarrow's Cato/Macros series for example. For readers of such series, this book is almost tailor made for them.

On the down side, this book is pretty expensive for a casual reader to buy and it doesn't go into much detail during the decline of Rome. But I don't think that was the real intent of the author.

Overall, an excellent effort by Adrian Goldworthy who wrote a really accessible reference book on the Roman legions during its heydays and make it interesting and informative enough that even veteran readers like myself or a novice who is only interested in fictional history, can both enjoy this book.

Detailed guide to Roman Army operations.......2007-02-07

This book is an excellent reference work on the structure and operations of the Roman Army, mostly covering the period of the Principate through Hadrian. What separates this book from others for me is that it does not focus merely on history or campaigns...I have plenty of other books that do that. This book on the other hand discusses in much detail things like:

- how a Roman fort is laid out
- what the officers and soldiers ate
- examples of duty rosters
- what training new recruits went through
- marriage and co-habitation
- pay scales including details like deductions for food and clothing

These are just examples of the detail that I have not seen compiled quite so well in one book.

Two negatives that I can think of and they are minor. Firstly, this is not a "scholarly" reference work and probably not suitable for graduate studies. Yet that may also be a virtue as it is the type of book that one can comfortably sit down and read straight through.

Secondly, the author is obviously British and a significant amount of his examples, charts, and photos relate specifically to Britannia. Now since a lot of very good archaeology comes from that province, that too is not a serious flaw and the author does make an effort to incorporate material from throughout the Empire.

A very worthy book for anyone interested in how the Roman Army actually worked!

Worth the money.......2006-12-16

I don't usually like books with heavy glossy pages because many publishers use that device to throw together a book that is heavy on photos and short on content. This is NOT the case here. Dr. Adrian Goldsworthy put together a great book, heavy on detail, well written and organized into a small package.

He devotes more effort into discussing the practical and operational evolution of the army than he does with the politics of the army. If you want to understand the political evolution of the army, this work will leave you short. But then again, that's not what the book is about.

As the Empire collapsed at its "ending", the tactics of its enemies had improved while the Roman Army hadn't evolved fast enough to meet the threat effectively. It would have been nice if Dr. Goldsworthy had taken some time to discuss this at greater length. But the book still gets 5 stars from me.

The Complete Roman Army.(Book Review) : An article from: The Historian

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The Complete Roman Army.(Book Review) : An article from: The Historian
John Dayton
Manufacturer: Thomson Gale
ProductGroup: Book
Binding: Digital
ASIN: B000B9DUDO
Release Date: 2005-09-03

Book Description

This digital document is an article from The Historian, published by Thomson Gale on March 22, 2005. The length of the article is 497 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: The Complete Roman Army.(Book Review)
Author: John Dayton
Publication: The Historian (Magazine/Journal)
Date: March 22, 2005
Publisher: Thomson Gale
Volume: 67 Issue: 1 Page: 155(1)

Article Type: Book Review

Distributed by Thomson Gale

Book Description

Here is a historical chronicle of the most powerful corporation in world history, beautifully illustrated with full-color paintings, photographs, and maps. Established by Royal Charter in 1600, the East India Company was, and remains to this day, the largest and most powerful multinational business the world has ever seen. It controlled over half the world's trade and a quarter of its population. It singlehandedly ruled India, raised its own army and navy, minted its own currency, and traded with every corner of the globe. It also trafficked in opium, greed, and brutal oppression, sowing the seeds that would lead to its downfall-and absorption by the British Crown.

The East India Company describes how "the Honourable Company" created its extraordinary trading empire by introducing an exotic cache of tea, silks, porcelain, cashmere, and spices to a luxury-starved England. It also explains how the company conducted its day-to-day business at home and in the East, through colorful figures such as Captain James Skinner and John Nicholson; how the opulent daily life of East India Company rulers amongst the ruled led to "the Mutiny"; and why India's first war of independence spelled an end not only to the company itself, but, eventually, to an entire empire.

Customer Reviews:

Excellent, well illustrated.......2005-05-26

This lavishly illustrated volume gives an excellent view of the East India Company - the experiences of the British in India, the spices and goods of interest to the West, and the history of the company over the centuries.

History that is Informative and Relevant.......2000-08-09

This book is deserving than more than just 5 stars.

As a historian myself, the biggest problem in expressing yourself is making "old" topics informative and interesting to modern generations. Antony Wild has succeeded beyond any scale of recognition in his book The East India Company: Trade and Conquest from 1600.

This book, which details the English East India Company's history will appeal to anyone with an interest in British, Indian, Asian, American, military, nautical, or commerical history-- it is that wide-ranging. This book is also a must-read for anyone interested or concerned over the so-called modern phenomenon of "globalization." After reading Wild's account, one can see that globalization has been around for nearly four hundred years, if not longer.

The English East India Company, acting under a royal charter from Queen Elizabeth I, sought entry into the Spice Trade in Asia. Soon, however, it found itself involved with Indian piece trade and trade from the Middle East and Arabia. Its trade interests in India eventually led to de facto conquest and colonization on that subcontinent-- all with the tacit support of the crown. The company reached into China and even North America-- it was East India Company tea that got dumped into Boston Harbor during the Tea Party.

The company exported and imported goods, laid the foundations for three important Indian cities, fought land wars and naval battles with other European merchant powers or local natives, and brought a host of new products and new words into the consciousness of the English-speaking world.

India proved to be the company's lasting legacy, and not always a positive one. However Wild provides a well-balanced account that does not paint the company as either completely ethical traders or imperialistic devils. No matter one's opinion, India proved to the company's (and Britain's) largest asset and also the cause for the company's eventual dissolution.

The book is well-illustrated and is an easy but very informative read. I would rank this amongst the top 10 books I have read in the last 5 years.

Book Description

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on a Gaussian space. Originally, it was developed to provide a probabilistic proof to HÃ¶rmander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis. This monograph presents the main features of the Malliavin calculus and discusses in detail its main applications. The author begins by developing the analysis on the Wiener space, and then uses this to establish the regularity of probability laws and to prove HÃ¶rmander's theorem. The regularity of the law of stochastic partial differential equations driven by a space-time white noise is also studied. The subsequent chapters develop the connection of the Malliavin with the anticipating stochastic calculus, studying anticipating stochastic differential equations and the Markov property of solutions to stochastic differential equations with boundary conditions. The second edition of this monograph includes recent applications of the Malliavin calculus in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.

Stochastic Partial Differential Equations (CHAPMAN & HALL/CRC APPLIED MATHEMATICS & NONLINEAR SCIENCE)

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Stochastic Partial Differential Equations (CHAPMAN & HALL/CRC APPLIED MATHEMATICS & NONLINEAR SCIENCE)
Pao-Liu Chow
Manufacturer: Chapman and Hall
ProductGroup: Book
Binding: Hardcover

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A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics)

ASIN: 1584884436

Book Description

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and ItÃ´'s equations, highlighting several computational and analytical techniques. Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way. The author first brings the subject back to its root in classical concrete problems. He then discusses a unified theory of stochastic evolution equations and describes a few applied problems, including the random vibration of a nonlinear elastic beam and invariant measures for stochastic Navier-Stokes equations. The book concludes by pointing out the connection of stochastic PDEs to infinite-dimensional stochastic analysis. By thoroughly covering the concepts and applications of stochastic PDEs at an introductory level, this text provides a guide to current research topics and lays the groundwork for further study.

Diffusions and Elliptic Operators (Probability and its Applications)

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Diffusions and Elliptic Operators (Probability and its Applications)
Richard F. Bass
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Probabilistic Techniques in Analysis (Probability and its Applications)

ASIN: 0387983155

Book Description

This is author-approved bcc: This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators. Martingale problems and the Malliavin calculus are presented in two other chapters. This book can be used as a textbook for a graduate course on diffusion theory with applications to PDE. It will also be a valuable reference to researchers in probability who are interested in PDE as well as for analysts who are interested in probabilistic methods. Richard F. Bass is Professor of Mathematics at the University of Washington. He has written many research papers on the topics covered by this book. Also Available: Richard F. Bass, Probabilistic Techniques in Analysis. Springer-Verlag New York, Inc, 0-387-94387-0

Probabilistic Models for Nonlinear Partial Differential Equations: Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) ... 22-30, 1995 (Lecture Notes in Mathematics)

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Probabilistic Models for Nonlinear Partial Differential Equations: Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) ... 22-30, 1995 (Lecture Notes in Mathematics)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.

Stochastic Partial Differential Equations : A Modeling, White Noise Functional Approach (Probability and Its Applications)

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A new approach to stochastic partial differential equations

Stochastic Partial Differential Equations : A Modeling, White Noise Functional Approach (Probability and Its Applications)
Helge Holden , Bernt Oksendal , Jan Uboe , and Tusheng Zhang
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817639284

Book Description

Stochastic methods have become increasingly important in the analysis of a broad range of phenomena in natural sciences and economics. Many processes are described by differential equations where some of the parameters and/or the initial data are not known with complete certainty due to lack of information, uncertainty in the measurements, or incomplete knowledge of the mechanisms themselves. To compensate for this lack of information one introduces stochastic noise in the equations, either in the parameters or in the initial data which results in stochastic differential equations.

At the same time there has been considerable development in the mathematical theory of stochastic differential equations which are used to model these phenomena. In this book the authors give a comprehensive introduction to stochastic partial differential equations. Their approach is based on white noise analysis, where the often ill-defined white noise, the derivative of the familiar Brownian motion, is introduced rigorously as the fundamental object.

First some of the mathematical background is discussed to provide the necessary tools to study several different stochastic partial differential equations. The techniques are primarily derived from functional analysis. The Wiener-Itô chaos expansion as well as the Itô/Skorohod integrals are developed in this setting, and properties of the Wick product and the Hermite transform are proved. The first applications are given to stochastic ordinary differential equations, e.g., the Volterra equation.

The main emphasis of the book is on stochastic partial differential equations. First the stochastic Poisson equation and the stochastic transport equation are discussed. Next, the authors consider the stochastic Schrödinger equation as well as the stochastic heat equation. The nonlinear Burgers' equation with a stochastic source is discussed, and finally the stochastic pressure equation, as well as other important equations are treated. The white noise approach often allows for solutions given by explicit formulas in terms of expectations of certain auxiliary processes. The noise in the above examples are all of Gaussian white noise type, but in the end the authors also show how to adapt the analysis to SPDEs involving noise of Poissonian type.

Customer Reviews:

A new approach to stochastic partial differential equations.......2000-07-21

SUMMARY: This book presents a new approach to stochastic partial differential equations based on white noise analysis. The framework makes heavy use of functional analysis and its main starting point is the Wiener chaos expansion and analogous expansions on different functional spaces (Schwartz spaces).

A stochastic PDE is a PDE containing a random noise term, which may be additive or multiplicative. One of the problems when working with Stochastic PDEs is to define a notion of solution which is meaningfully extendable to the nonlinear case. Problems arises because the noise term is highly irregular: for each sample of the noise, one has a (nonlinear) PDE with a very irregular term in it. In physical terms, one may encounter "ultraviolet" divergences. So, one is first faced with an existence/ unicity problem for such equations. Additionally, one would like to describe probabilitic properties of such solutions.

The method proposed by the authors can be described as follows: first, one expands the noise term in the PDE using a Wiener chaos expansion. Truncating the expansion at a certain order n yields a "regularized" equation in which the noise is smoothened. This can be roughly described as an ultraviolet cutoff. The equation then has a unique solution in an appropriate functional space. The solution of the original SPDE is then defined as the sequence of truncated solutions. In some cases, this sequence may converge in some classical sense in an appropriate function space to a weak or strong solution defined in the usual sense. But, in general, this is not the case and the notion of solution defined by the authors may be different from classical notions.

Although the title contains the word 'modeling', it may look as the abstract definition of solution proposed by the authors may have little to do with the physical notion of solution. One feels a need for a justification why this definition of a solution is physically relevant at all, which I feel is lacking. The authors give some examples, such as the noisy Burgers equation and the Kardar-Parisi-Zhang equation, but the results predicted for the solutions seem to be different than the ones predicted for example by renormalization group analysis for example regarding the scaling exponents for KPZ. Also, it would be interesting to compare this notion of solution with more classical ones for example using the semigroup/ Green function approach.

The approach proposed bears a strong resemblance to ultraviolet regularization schemes used in renormalization group theory. In fact, this framework may be seenas a probabilistic setting for renormalization methods.Unfortunately there is little discussion of this point in the book.

The first chapters contain an interesting review of white noise expansions and chaos expansions, useful in their own interest.

Book Description

This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; and invariant measures for specific models. The focus is on models of dynamical processes affected by white noise, which are described by partial differential equations such as the reaction-diffusion equations or Navier-Stokes equations. Besides existence and uniqueness questions, the authors pay special attention to the asymptotic behavior of the solutions, to invariant measures and ergodicity. The authors present some of the results found here for the first time. For all whose research interests involve stochastic modeling, dynamical systems, or ergodic theory, this book will be an essential purchase.

Spatial Branching Processes, Random Snakes And Partial Differntial Equations (Lecture Notes Series)

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Spatial Branching Processes, Random Snakes And Partial Differntial Equations (Lecture Notes Series)
J. LeGall
Manufacturer: Birkhauser Boston
ProductGroup: Book
Binding: Paperback

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ASIN: 3764361263

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The text includes a presentation of the measure-valued branching processes also called superprocesses and of their basic properties. In the important quadratic branching case, the path-valued process known as the Brownian snake is used to give a concrete and powerful representation of superprocesses. This representation is applied to several connections with a class of semilinear partial differential equations. On the one hand, these connections give insight into properties of superprocesses. On the other hand, the probabilistic point of view sometimes leads to new analytic results, concerning for instance the trace classification of positive solutions in a smooth domain. An important tool is the analysis of random trees coded by linear Brownian motion. This includes the so-called continuum random tree and leads to the fractal random measure known as ISE, which has appeared recently in several limit theorems for models of statistical mechanics. This book is intended for postgraduate students and researchers in probability theory. It will also be of interest to mathematical physicists or specialists of PDE who want to learn about probabilistic methods. No prerequisites are assumed except for some familiarity with Brownian motion and the basic facts of the theory of stochastic processes. Although the text includes no new results, simplified versions of existing proofs are provided in several instances.

Advances in Nonlinear Partial Differential Equations and Stochastics (Series on Advances in Mathematics for Applied Sciences)

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Advances in Nonlinear Partial Differential Equations and Stochastics (Series on Advances in Mathematics for Applied Sciences)

Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810233965

Advances in Nonlinear Partial Differential Equations: A Volume in Honor of Professor Xiaqi Ding (Series on Advances in Mathematics for Applied Sciences)

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Advances in Nonlinear Partial Differential Equations: A Volume in Honor of Professor Xiaqi Ding (Series on Advances in Mathematics for Applied Sciences)

Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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Amplitude Equations for Stochastic Partial Differential Equations (Interdisciplinary Mathematical Sciences) (Interdisciplinary Mathematical Sciences)

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Amplitude Equations for Stochastic Partial Differential Equations (Interdisciplinary Mathematical Sciences) (Interdisciplinary Mathematical Sciences)
Dirk Blomker
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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Product Description

Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap. The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability. For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.

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