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From Brownian Motion to Schrödinger’s Equation

  • Book
  • © 1995

Overview

Authors:
  1. Kai Lai Chung

    1. Department of Mathematics, Stanford University, Stanford, USA

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  2. Zhongxin Zhao
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  • 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

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 312)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XII
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  2. Preparatory Material

    • Kai Lai Chung, Zhongxin Zhao
    Pages 1-29

  3. Killed Brownian Motion

    • Kai Lai Chung, Zhongxin Zhao
    Pages 31-60

  4. Schrödinger Operator

    • Kai Lai Chung, Zhongxin Zhao
    Pages 61-102

  5. Stopped Feynman-Kac Functional

    • Kai Lai Chung, Zhongxin Zhao
    Pages 103-130

  6. Conditional Brownian Motion and Conditional Gauge

    • Kai Lai Chung, Zhongxin Zhao
    Pages 131-158

  7. Green Functions

    • Kai Lai Chung, Zhongxin Zhao
    Pages 159-190

  8. Conditional Gauge and q-Green Function

    • Kai Lai Chung, Zhongxin Zhao
    Pages 191-213

  9. Various Related Developments

    • Kai Lai Chung, Zhongxin Zhao
    Pages 215-240

  10. The Case of One Dimension

    • Kai Lai Chung, Zhongxin Zhao
    Pages 241-279

  11. Back Matter

    Pages 281-290
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Keywords

About this book

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.

Reviews

"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

Authors and Affiliations

  • Department of Mathematics, Stanford University, Stanford, USA

    Kai Lai Chung

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