An Introduction to Stochastic Filtering Theory

Front Cover
OUP Oxford, Apr 17, 2008 - Business & Economics - 270 pages
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 filteringmodels 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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Introduction
1
2 Brownian motion and martingales
15
3 Stochastic integrals and Its formula
36
4 Stochastic differential equations
61
5 Filtering model and KallianpurStriebel formula
82
6 Uniqueness of the solution for Zakais equation
96
7 Uniqueness of the solution for the filtering equation
121
8 Numerical methods
132
9 Linear filtering
157
10 Stability of nonlinear filtering
186
11 Singular filtering
231
Bibliography
255
List of Notations
266
Index
269
Copyright

Other editions - View all

Common terms and phrases

About the author (2008)


Jie Xiong received his PhD in Statistics from the University of North Carolina in 1992. He accepted a position as Associate Professor in the University of Tennessee in 1993, and remains a professor in the Department of Mathematics. Besides many short visits to other institutes, he spent six months visiting the University of Wisconsin, another six months visiting the Fields Institute in Toronto, a year working in the University of Alberta as a Tier II Canada Research Chair in Stochastic Processes and Filtering, and one year in Weierstrass Institute in Berlin supported by a Humboldt Research Fellowship. Currently, he serves on the editorial board of the journal Communication on Stochastic Analysis.

Bibliographic information