Large Deviations Techniques and Applications (Stochastic Modelling and Applied Probability Book 38) 2nd Edition by Amir Dembo (PDF)

Description

Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences.The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As part of postdoc work I wanted to study large deviations for solutions to PDE/ODE with random coefficients (not the usual additive stochastic noise). So I bought this book and read chapters 1, 2, 4, and parts of 3, 5, and 6).This book provided “all” that I needed in order to obtain a simple result. In other words, after reading these chapters and doing some exercises one understands the common tricks and proof techniques needed. The chapters are well organized so one can for example read 1 and 2 and then understand the LDP for sums of independent random variables.This book requires some commitment. For example, before getting into any interesting results, technical definitions such as “exponential tightness” are introduced. In contrast, Varadhan’s lecture notes give you a general intuition and feeling for the important results right from the start (though I can’t comment on how cleanly Varadhan fills in the details).So buy this book not for an easy overview, but because you want to learn the techniques. Or maybe buy this book because you already know some techniques, in which case you could quickly scan the chapters and thus give yourself an overview.P.S. The obligatory back-page comment on how some of the book can be read with “little more than basic calculus…” is (as always) completely false 🙂

⭐Maybe this is the only book which treats “Large deviation” so thoroughly and so rigorously. Many other books cite this one for further details. However, this book is very difficult to read. People, like me, with graduate level probability knowledge, will still feel difficult to follow. It is not all due to the presentation of this book. It may partially because the “theory of large deviation” itself is not in a good shape. So this book is not good one for self-study but might be a good reference.

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