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Birkhäuser

Real and Stochastic Analysis

New Perspectives

  • Book
  • © 2004

Overview

Editors:
  1. M. M. Rao

    1. Department of Mathematics, University of California, Riverside, USA

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  • Self-contained and written by active researchers, each chapter is devoted to a particular application of functional analytic methods in stochastic analysis
  • Every chapter contains substantial new results as well as a clear, unified account of the existing theory, relevant references and numerous open problems
  • Especially valuable as a seminar text for dissertation-level graduate students and as a reference

Part of the book series: Trends in Mathematics (TM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction and Outline

    • M. M. Rao
    Pages 1-7

  3. Stochastic Differential Equations and Hypoelliptic Operators

    • Denis R. Bell
    Pages 9-42

  4. Curved Wiener Space Analysis

    • Bruce K. Driver
    Pages 43-198

  5. Noncommutative Probability and Applications

    • Stanley Gudder
    Pages 199-238

  6. Advances and Applications of the Feynman Integral

    • Brain Jefferies
    Pages 239-303

  7. Stochastic Differential Equations Based on Lévy Processes and Stochastic Flows of Diffeomorphisms

    • Hiroshi Kunita
    Pages 305-373

  8. Convolutions of Vector Fields-III: Amenability and Spectral Properties

    • M. M. Rao
    Pages 375-401

  9. Back Matter

    Pages 403-405
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Keywords

About this book

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov­ ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil­ ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Reviews

"Although most of the papers contain new results and/or proofs, their authors tried to make them reasonably self-contained and provide a wide background to the problems studied, so the papers should be accessible to advanced graduate students and serve as an introduction to some topics which have been paid considerable attention recently."

—Applications of Mathematics

Editors and Affiliations

  • Department of Mathematics, University of California, Riverside, USA

    M. M. Rao

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