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Stochastic Differential Equations: An Introduction with Applications, 6th Edition

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Stochastic Differential Equations: An Introduction with Applications, 6th Edition Cover

ISBN13: 9783540047582
ISBN10: 3540047581
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Synopses & Reviews

Publisher Comments:

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. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.

Synopsis:

  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.

Synopsis:

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. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten.

Table of Contents

Introduction.- Some Mathematical Preliminaries.- Itô Integrals.- Itô 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.

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satyabasak, May 2, 2007 (view all comments by satyabasak)
Its a very good book to built a solid background on Stochastic Differential Equation. Clarity, Objectivity and freindlyness are the important qualities of this book. I would love to read this book.
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Product Details

ISBN:
9783540047582
Author:
Oksendal, Bernt
Publisher:
Springer
Author:
Øksendal, Bernt
Author:
Ksendal, B. K.
Author:
A~ksendal, Bernt
Location:
Berlin, Heidelberg
Subject:
Differential Equations
Subject:
Stochastic differential equations
Subject:
Probability & Statistics - General
Subject:
Mathematics | Probability and Statistics
Subject:
Statistics
Subject:
MSC(2000):60G35, 60G40, 60H10, 60J45, 93E20
Subject:
filtering theory
Subject:
Mathematical finance
Subject:
Optimal filtering
Subject:
stochastic calculus
Subject:
Stochastic Control
Subject:
Probability Theory and Stochastic Processes
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Systems Theory, Control
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Economic theory
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Systems theory.
Subject:
Mathematical optimization
Subject:
Differential equations, partial
Subject:
Economics
Copyright:
Edition Number:
6
Edition Description:
2003. Corr. 3rd
Series:
Universitext
Series Volume:
no. 472
Publication Date:
20100922
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
384
Dimensions:
235 x 155 mm 1210 gr

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Related Subjects

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Stochastic Differential Equations: An Introduction with Applications, 6th Edition New Trade Paper
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Product details 384 pages Springer - English 9783540047582 Reviews:
"Synopsis" by ,   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.
"Synopsis" by , 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. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten.
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