An Introduction to Partial Differential Equations for Probabilists

Cambridge Studies in Advanced Mathematics #112

by Daniel W. Stroock

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 easy to understand for 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 Hormander.

Genres: Mathematics

215 pages, ebook

First published April 28, 2008