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Stochastic differential equations : an introduction with applications / Bernt Øksendal.
Author
Øksendal, B. K. (Bernt Karsten), 1945-
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Format
Book
Language
English
Εdition
4th ed.
Published/Created
Berlin ; New York : Springer, ©1995.
Description
xvi, 271 pages : illustrations ; 24 cm.
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
ReCAP - Remote Storage
QA274.23 .O47 1995
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Details
Subject(s)
Stochastic differential equations
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Series
Universitext
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Summary note
The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications..." The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about.
Bibliographic references
Includes bibliographical references (p. [252]-260) and index.
Contents
1. Introduction
2. Some mathematical preliminaries
3. Ito integrals
4. Ito processes and the Ito formula
5. Stochastic differential equations
6. The filtering problem
7. Diffusions: basic properties
8. Other topics in diffusion theory
9. Applications to boundary value problems
10. Applications to optimal stopping
11. Applications to stochastic control
Appendix A. Normal random variables
Appendix B. Conditional expectations
Appendix C. Uniform integrability and Martingale convergences.
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ISBN
3540602437 ((Berlin ; : soft ; : acid-free paper))
9783540602439 ((Berlin ; : soft ; : acid-free paper))
0387602437 ((New York ; : soft ; : acid-free paper))
9780387602431 ((New York ; : soft ; : acid-free paper))
LCCN
95037627
OCLC
32968575
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