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  3. Partial Differential Equations for Probabilists
  • Cited by 19
Publisher:
Cambridge University Press
Online publication date:
July 2010
Print publication year:
2008
Online ISBN:
9780511755255
DOI:
https://doi.org/10.1017/CBO9780511755255
Subjects:
Mathematics (general), Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Studies in Advanced Mathematics (112)
Information

Book description

This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given new proofs designed for readers with limited expertise in analysis. The author covers the theory of linear, second order, partial differential equations of parabolic and elliptic types. Many of the techniques have antecedents in probability theory, although the book also covers a few purely analytic techniques. In particular, a chapter is devoted to the De Giorgi–Moser–Nash estimates, and the concluding chapter gives an introduction to the theory of pseudodifferential operators and their application to hypoellipticity, including the famous theorem of Lars Hormander.

Reviews

‘The book will capture your attention with elegant proofs presented in an almost perfectly self-contained manner, with abundant talk in a lecturer's tone by the author himself, but with a little bit of an aficionado's taste. The book, arranged idiosyncratically, has such a strong impact that, at the next moment, you may find yourself carried away in looking for mathematical treasures scattered here and there in each chapter. The reviewer recommends the present book with confidence to anyone who in interested in PDE and probability theory. At least you should always keep this at your side if you are a probabilist at all.'

Isamu Doku Source: Mathematical Reviews

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