An Introduction to Stochastic Filtering Theory

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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.

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1 Introduction
2 Brownian motion and martingales
3 Stochastic integrals and Its formula
4 Stochastic differential equations
5 Filtering model and KallianpurStriebel formula
6 Uniqueness of the solution for Zakais equation
7 Uniqueness of the solution for the filtering equation
8 Numerical methods
9 Linear filtering
10 Stability of nonlinear filtering
11 Singular filtering
List of Notations

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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.

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