Book Search:  

 

 
Google full text of our books:

bookjacket

Markov Processes from K. Itô's Perspective (AM-155)
Daniel W. Stroock

Paperback | 2003 | $72.50 / £50.00 | ISBN: 9780691115436
288 pp. | 6 x 9
| SHOPPING CART

eBook | ISBN: 9781400835577 |
Our eBook editions are available from these online vendors

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program.

The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported.

The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Link:

Series:

Subject Area:

VISIT OUR MATH WEBSITE

Shopping Cart:

  • For ebooks:

When this eBook becomes available, we will provide direct links to buy it. Until then,
check pre-order availability at these e-tailer sites by copying and pasting the eISBN
9781400835577:

Shopping Cart:

  • For hardcover/paperback orders:

    For hardcover/paperback orders in the United States, Canada, Latin America, Asia, and Australia

    Paperback: $72.50 ISBN: 9780691115436

    For hardcover/paperback orders in Europe, Africa, the Middle East, and India

    Paperback: £50.00 ISBN: 9780691115436

    Prices subject to change without notice

    File created: 7/11/2014

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Princeton APPS
Sample Chapters
Subjects
Series
Catalogs
Princeton Legacy Library
Textbooks
Media/Reviewers
Class Use
Rights/Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share
Send me emails
about new books in:
Mathematics
More Choices
Email:
Country:
Name: