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Multidimensional Diffusion Processes

  • Book
  • © 2006

Overview

Authors:
  1. Daniel W. Stroock

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  2. S. R. Srinivasa Varadhan

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

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    You can also search for this author in PubMed   Google Scholar

  • Applies martingale theory to the theory of Markov processes
  • Presents proofs and techniques in an easily adaptable style
  • Introductory summaries of standard probability theory and measure theory review basic knowledge before launching more sophisticated concepts
  • Recommended for graduate students, research workers and readers interested in Markov processes from a theoretical point of view
  • Includes supplementary material: sn.pub/extras

Part of the book series: Classics in Mathematics (CLASSICS)

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Table of contents (13 chapters)

  1. Front Matter

    Pages N1-XII
    Download chapter PDF

  2. Introduction

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 1-6

  3. Preliminary Material: Extension Theorems, Martingales, and Compactness

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 7-45

  4. Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 46-64

  5. Parabolic Partial Differential Equations

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 65-81

  6. The Stochastic Calculus of Diffusion Theory

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 82-121

  7. Stochastic Differential Equations

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 122-135

  8. The Martingale Formulation

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 136-170

  9. Uniqueness

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 171-194

  10. Itô’s Uniqueness and Uniqueness to the Martingale Problem

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 195-207

  11. Some Estimates on the Transition Probability Functions

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 208-247

  12. Explosion

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 248-260

  13. Limit Theorems

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 261-284

  14. The Non-unique Case

    • Daniel W. Stroock, S. R. Srinivasa Varadhan
    Pages 285-303

  15. Back Matter

    Pages 304-338
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About this book

"This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. (...) The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. (...) The reader must be familiar with standard probability theory and measure theory which are summarized at the beginning of the book. This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik, 1981

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Daniel W. Stroock

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    S. R. Srinivasa Varadhan

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