Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov's formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.

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Information

Publisher

Academic Press

Year

2014

ISBN

9781483217871

Topic

Mathematics

Subtopic

Probability & Statistics

Index

Mathematics

Front Cover
Stochastic Differential Equations and Applications
Copyright Page
Table of Contents
Preface
General Notation
Contents of Volume 2
Chapter 1. Stochastic Processes
Chapter 2. Markov Processes
Chapter 3. Brownian Motion
Chapter 4. The Stochastic Integral
Chapter 5. Stochastic Differential Equations
Chapter 6. Elliptic and Parabolic Partial Differential Equations and Their Relations to Stochastic Differential Equations
Chapter 7. The Cameron–Martin–Girsanov Theorem
Chapter 8. Asymptotic Estimates for Solutions
Chapter 9. Recurrent and Transient Solutions
References
Index