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Description of Stochastic Differential Equations |
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 such fields as 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 in order to quickly progress to the parts of the theory that are 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.
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Contents of Stochastic Differential Equations |
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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