From Brownian Motion to Schrödinger’s Equation (Grundlehren der mathematischen Wissenschaften, 312)

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. Front Matter....Pages I-XII Preparatory Material....Pages 1-29 Killed Brownian Motion....Pages 31-60 Schrödinger Operator....Pages 61-102 Stopped Feynman-Kac Functional....Pages 103-130 Conditional Brownian Motion and Conditional Gauge....Pages 131-158 Green Functions....Pages 159-190 Conditional Gauge and q -Green Function....Pages 191-213 Various Related Developments....Pages 215-240 The Case of One Dimension....Pages 241-279 Back Matter....Pages 281-290 Die Theorie der Brown'schen Bewegung hat sich in letzter Zeit zu einem sehr wichtigen Werkzeug bei der Losung von Problemen in der mathematischen Physik entwickelt. In der vorliegenden, in sich abgeschlossenen und sehr gut lesbaren Abhandlung haben die zwei auf diesem Gebiet fuhrenden Autoren besonderen Wert auf Klarheit der Ausfuhrung gelegt. In this chapter we collect together a number of introductory topics for later use. Kai Lai Chung, Zhongxin Zhao. Includes Bibliographical References And Index.