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Large Deviations Techniques and Applications Paperback – Nov 18 2009

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4 of 4 people found the following review helpful
Great book. Gives "all" the details. Requires some commitment. March 23 2011
By Ian Langmore - Published on
Format: Paperback
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 :)
2 of 6 people found the following review helpful
A thorough treatment. But too difficult April 19 2010
By Yan Zhu - Published on
Format: Paperback
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.