An Introduction to Stochastic Filtering Theory
Series: Oxford Graduate Texts in Mathematics; 18;
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Product details:
- Publisher OUP Oxford
- Date of Publication 17 April 2008
- ISBN 9780199219704
- Binding Hardback
- No. of pages286 pages
- Size 242x162x22 mm
- Weight 556 g
- Language English 0
Categories
Short description:
Stochastic filtering theory is a field that has seen a rapid development in recent years and this book, aimed at graduates and researchers in applied mathematics, provides an accessible introduction covering recent developments.
MoreLong description:
Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance.
As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results.
In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.
It is a timely account of the field suitable for serious researchers in stochastic analysis.
Table of Contents:
Preface
Introduction
Brownian motion and martingales
Stochastic integrals and Itô's formula
Stochastic differential equations
Filtering model and Kallianpur-Striebel formula
Uniqueness of the solution for Zakai's equation
Uniqueness of the solution for the filtering equation
Numerical methods
Linear filtering
Stability of nonlinear filtering
Singular filtering
Bibliography
Index
