Classics in Mathematics

Multidimensional Diffusion Processes

Authors: Stroock, Daniel W., Varadhan, S.R.S.

  • 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
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eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-28999-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-662-22201-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

From the reviews:

"… Both the Markov-process approach and the Itô approach … have been immensely successful in diffusion theory. The Stroock-Varadhan book, developed from the historic 1969 papers by its authors, presents the martingale-problem approach as a more powerful - and, in certain regards, more intrinsic-means of studying the foundations of the subject. […] … the authors make the uncompromising decision not "to proselytise by intimidating the reader with myriad examples demonstrating the full scope of the techniques", but rather to persuade the reader "with a careful treatment of just one problem to which they apply". […] Most of the main tools of stochastic-processes theory are used, ..but it is the formidable combination of probability theory with analysis … which is the core of the work. […] I have emphasized the great importance of the Stroock-Varadhan book. It contains a lot more than I have indicated; in particular, its many exercises conain much interesting material.
For immediate confirmation of the subject’s sparkle, virtuosity, and depth, see … McKean (‘s 1969 book). The Stroock-Varadhan book proceeds on its inexorable way like a massive Bach fugue. … But old J.S. can e something of knockout if his themes get hold of you. And his influence on what followed was 8you may say) substantial."
David Williams in the Bulletin of the American Mathematical Society

Table of contents (13 chapters)

  • Introduction

    Stroock, Daniel W. (et al.)

    Pages 1-6

  • Preliminary Material: Extension Theorems, Martingales, and Compactness

    Stroock, Daniel W. (et al.)

    Pages 7-45

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

    Stroock, Daniel W. (et al.)

    Pages 46-64

  • Parabolic Partial Differential Equations

    Stroock, Daniel W. (et al.)

    Pages 65-81

  • The Stochastic Calculus of Diffusion Theory

    Stroock, Daniel W. (et al.)

    Pages 82-121

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-28999-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-662-22201-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Multidimensional Diffusion Processes
Authors
Series Title
Classics in Mathematics
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-28999-9
DOI
10.1007/3-540-28999-2
Softcover ISBN
978-3-662-22201-0
Series ISSN
1431-0821
Edition Number
1
Number of Pages
XII, 338
Additional Information
Reprint of the 1997 Edition (Grundlehren der mathematischen Wissenschaften, Vol. 233)
Topics