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Stochastic differential equations : an introduction with applications

Author: B K Øksendal
Publisher: Berlin ; New York : Springer, ©2003.
Series: Universitext.
Edition/Format:   eBook : Document : English : 6th edView all editions and formats
Summary:
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Øksendal, Bernt.
Stochastic differential equations.
Berlin ; New York : Springer, ©2003
(DLC) 2003052637
(OCoLC)52203046
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: B K Øksendal
ISBN: 9783642143946 3642143946
OCLC Number: 778368218
Description: 1 online resource (xxiii, 360 pages) : illustrations.
Contents: Introduction --
Some Mathematical Preliminaries --
It Integrals --
It Formula and the Martingale Representation Theorem --
Stochastic Differential Equations --
The Filtering Problem --
Diffusions: Basic Properties --
Other Topics in Diffusion Theory --
Applications to Boundary Value Problems --
Applications to Optimal Stopping --
Application to Stochastic Control --
Application to Mathematical Finance --
Appendix A: Normal Random Variables --
Appendix B: Conditional Expectations --
Appendix C: Uniform Integrability and Martingale Convergence --
Appendix D: An Approximation Result --
Solutions and Additional Hints to Some of the Exercises --
References --
List of Frequently Used Notation and Symbols --
Index.
Series Title: Universitext.
Responsibility: Bernt Øksendal.

Abstract:

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. This corrected 6th printing of the 6th edition contains additional corrections and useful improvements, based in part on helpful comments from the readers.

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