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Introduction to Stochastic Filtering Theory

Introduction to Stochastic Filtering Theory
Author
Xiong, Jie 
Publisher
Oxford Univ Pr on Demand 
Publication Date
Sep, 2008 
ISBN
0199219702 or 9780199219704
HARDCOVER 
270 Pages
出版済み 3-5週間でお届けいたします。
The delivery time takes 3 to 5 weeks

¥ 12,962 (tax included)

Description

An up-to-date reference on a topical subject
The author is a well-regarded researcher in the field
Each chapter on filtering contains a historical note
Methods introduced can be applied to more general stochastic partial differential equations

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.

Contents

1. Introduction
2. Brownian motion and martingales
3. Stochastic intervals and Ito's formula
4. Stochastic differential equations
5. Filtering model and Kallianpur-Striebel formula
6. Uniqueness of the solution for Zakai's equation
7. Uniqueness of the solution for the filtering equation
8. Numerical methods
9. Linear filtering
10. Stability of nonlinear filtering
11. Singular filtering

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