In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics.
A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.

stopping time" throughout, without which, in the words of Chung, "many claimed probability attempts are really only old analysis in disguise" Specially for readers who want to see how probability is applied to analysis and mathematical physics Includes supplementary material: sn.pub/extras

Zusammenfassung
"This book is an excellent contribution to potential theory and stochastic processes, and recommended to researchers and graduate students of mathematics and mathematical physics." - M. Nagasawa, Universität Zürich

Inhalt

1. Preparatory Material.- 2. Killed Brownian Motion.- 3. Schrödinger Operator.- 4. Stopped Feynman-Kac Functional.- 5. Conditional Brownian Motion and Conditional Gauge.- 6. Green Functions.- 7. Conditional Gauge and q-Green function.- 8. Various Related Developments.- 9. The Case of One Dimension.- References.