Fundamentals of Stochastic Filtering / Edition 1

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This book provides a rigorous mathematical treatment of the non-linear shastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of shastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of shastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

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Editorial Reviews

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From the reviews:

“This book provides a rigorous mathematical treatment of the nonlinear shastic filtering problem with particular emphasis on numerical methods. … The text is essentially self-contained … . In an appendice the required results from measure theory and shastic analysis are stated and proved. Intended readers are researchers and graduate students that have an interest in theoretical aspects of shastic filtering. The text is supplemented with many exercises and detailed solutions. … a standard reference for teaching and working in the field of shastic filtering.” (H. M. Mai, Zentralblatt MATH, Vol. 1176, 2010)

“This book is one of the few books dealing with both the theoretical foundations and modern shastic particle techniques in shastic filtering through the entire text. … I highly recommend this book to any researcher in applied mathematics, as well as to any researchers in engineering and computer sciences with some background in statistics and probability. … The book can also serve as a useful text for an informal seminar or a second year graduate course on shastic filtering.” (Pierre Del Moral, Bulletin of the American Mathematical Society, Vol. 48 (2), April, 2011)

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Product Details

  • ISBN-13: 9781441926425
  • Publisher: Springer New York
  • Publication date: 11/19/2010
  • Series: Stochastic Modelling and Applied Probability Series, #60
  • Edition description: Softcover reprint of hardcover 1st ed. 2009
  • Edition number: 1
  • Pages: 390
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.83 (d)

Table of Contents

Filtering Theory.- The Shastic Process—.- The Filtering Equations.- Uniqueness of the Solution to the Zakai and the Kushner–Stratonovich Equations.- The Robust Representation Formula.- Finite-Dimensional Filters.- The Density of the Conditional Distribution of the Signal.- Numerical Algorithms.- Numerical Methods for Solving the Filtering Problem.- A Continuous Time Particle Filter.- Particle Filters in Discrete Time.

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