Introduction to Stochastic Filtering Theory

Hardcover | June 30, 2008

byJie Xiong

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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.

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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...

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,...

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Kobo ebook|May 6 2013

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Format:HardcoverDimensions:224 pages, 9.21 × 6.14 × 0.87 inPublished:June 30, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199219702

ISBN - 13:9780199219704

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Table of Contents

Preface1. Introduction2. Brownian motion and martingales3. Stochastic intervals and Ito's formula4. Stochastic differential equations5. Filtering model and Kallianpur-Striebel formula6. Uniqueness of the solution for Zakai's equation7. Uniqueness of the solution for the filtering equation8. Numerical methods9. Linear filtering10. Stability of nonlinear filtering11. Singular filteringBibliographyIndex