Partial Differential Equations for Probabilists

Know about the book -

Partial Differential Equations for Probabilists is written by Daniel W. Stroock and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 0511755252 (ISBN 10) and 9780511755255 (ISBN 13).

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 type. 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 DeGiorgi-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 Hörmander.