© 2009

Fundamentals of Stochastic Filtering


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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction

    1. Alan Bain, Dan Crisan
      Pages 1-9
  3. Filtering Theory

    1. Front Matter
      Pages 11-11
    2. Alan Bain, Dan Crisan
      Pages 13-45
    3. Alan Bain, Dan Crisan
      Pages 47-93
    4. Alan Bain, Dan Crisan
      Pages 127-139
    5. Alan Bain, Dan Crisan
      Pages 141-163
    6. Alan Bain, Dan Crisan
      Pages 165-188
  4. Numerical Algorithms

    1. Front Matter
      Pages 189-189
    2. Alan Bain, Dan Crisan
      Pages 191-220
    3. Alan Bain, Dan Crisan
      Pages 221-256
    4. Alan Bain, Dan Crisan
      Pages 257-290
  5. Back Matter
    Pages 291-390

About this book


The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic 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 stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices.

The book is intended as a reference for graduate students and researchers interested in the field. It is also suitable for use as a text for a graduate level course on stochastic filtering. Suitable exercises and solutions are included.


Filtering Fundamentals Modeling Probability theory Stochastic Stochastic Processes algorithms calculus filtering problem measure theory stochastic process

Authors and affiliations

  1. 1.BNP Paribas 10 Harewood AvLondonUnited Kingdom
  2. 2.Department of MathematicsImperial College London 180 Queen’s GateLondonUnited Kingdom

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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)