Diffusions and Elliptic Operators (Probability and Its Applications) - Hardcover

Bass, Richard F.

Hardcover

ISBN 10: 0387983155 ISBN 13: 9780387983158

Publisher: Springer, 1997

Synopsis

This book will serve as a reference book for graduate students and researchers in probability theory or partial differential equations who want to learn more about the interplay of these two areas.

About this title

Synopsis

This is author-approved bcc: This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators. Martingale problems and the Malliavin calculus are presented in two other chapters. This book can be used as a textbook for a graduate course on diffusion theory with applications to PDE. It will also be a valuable reference to researchers in probability who are interested in PDE as well as for analysts who are interested in probabilistic methods. Richard F. Bass is Professor of Mathematics at the University of Washington.

He has written many research papers on the topics covered by this book. Also Available: Richard F. Bass, Probabilistic Techniques in Analysis. Springer-Verlag New York, Inc, 0-387-94387-0

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0387983155
• ISBN 13: 9780387983158
• Binding: Hardcover
• Number of pages: 246