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Fundamentals of Stochastic Filtering

  • Book
  • © 2009

Overview

Authors:
  1. Alan Bain

    1. BNP Paribas 10 Harewood Av, London, United Kingdom

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  2. Dan Crisan

    1. Department of Mathematics, Imperial College London 180 Queen’s Gate, London, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  • The authors are an authority in the stochastic filtering field
  • An assortment of Measure Theory, Probability Theory and Stochastic Analysis results are included in order to make this book as self contained as possible
  • Exercises and solutions included throughout

Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 60)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    1. Introduction

      • Alan Bain, Dan Crisan
      Pages 1-9

  3. Filtering Theory

    1. Front Matter

      Pages 11-11
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    2. The Stochastic Process π

      • Alan Bain, Dan Crisan
      Pages 13-45

    3. The Filtering Equations

      • Alan Bain, Dan Crisan
      Pages 47-93

    4. Uniqueness of the Solution to the Zakai and the Kushner–Stratonovich Equations

      • Alan Bain, Dan Crisan
      Pages 95-126

    5. The Robust Representation Formula

      • Alan Bain, Dan Crisan
      Pages 127-139

    6. Finite-Dimensional Filters

      • Alan Bain, Dan Crisan
      Pages 141-163

    7. The Density of the Conditional Distribution of the Signal

      • Alan Bain, Dan Crisan
      Pages 165-188

  4. Numerical Algorithms

    1. Front Matter

      Pages 189-189
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    2. Numerical Methods for Solving the Filtering Problem

      • Alan Bain, Dan Crisan
      Pages 191-220

    3. A Continuous Time Particle Filter

      • Alan Bain, Dan Crisan
      Pages 221-256

    4. Particle Filters in Discrete Time

      • Alan Bain, Dan Crisan
      Pages 257-290

  5. Back Matter

    Pages 291-390
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Keywords

About this book

Many aspects of phenomena critical to our lives can not be measured directly. Fortunately models of these phenomena, together with more limited obs- vations frequently allow us to make reasonable inferences about the state of the systems that a?ect us. The process of using partial observations and a stochastic model to make inferences about an evolving system is known as stochastic ?ltering. The objective of this text is to assist anyone who would like to become familiar with the theory of stochastic ?ltering, whether graduate student or more experienced scientist. The majority of the fundamental results of the subject are presented using modern methods making them readily available for reference. The book may also be of interest to practitioners of stochastic ?ltering, who wish to gain a better understanding of the underlying theory. Stochastic ?ltering in continuous time relies heavily on measure theory, stochasticprocessesandstochasticcalculus.Whileknowledgeofbasicmeasure theory and probability is assumed, the text is largely self-contained in that the majority of the results needed are stated in two appendices. This should make it easy for the book to be used as a graduate teaching text. With this in mind, each chapter contains a number of exercises, with solutions detailed at the end of the chapter.

Reviews

From the reviews:

“This book provides a rigorous mathematical treatment of the nonlinear stochastic filtering problem with particular emphasis on numerical methods. … The text is essentially self-contained … . In an appendice the required results from measure theory and stochastic analysis are stated and proved. Intended readers are researchers and graduate students that have an interest in theoretical aspects of stochastic filtering. The text is supplemented with many exercises and detailed solutions. … a standard reference for teaching and working in the field of stochastic 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 stochastic particle techniques in stochastic 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 stochastic filtering.” (Pierre Del Moral, Bulletin of the American Mathematical Society, Vol. 48 (2), April, 2011)

Authors and Affiliations

  • BNP Paribas 10 Harewood Av, London, United Kingdom

    Alan Bain

  • Department of Mathematics, Imperial College London 180 Queen’s Gate, London, United Kingdom

    Dan Crisan

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