Fundamentals of Stochastic Filtering / Edition 1

by Alan Bain, Dan Crisan

Overview

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 affect us. The process of using partial observations and a shastic model to make inferences about an evolving system is known as shastic—ltering. The objective of this text is to assist anyone who would like to become familiar with the theory of shastic—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 shastic—ltering, who wish to gain a better understanding of the underlying theory. Shastic—ltering in continuous time relies heavily on measure theory, shasticprocessesandshasticcalculus.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.

Product Details

ISBN-13:	9781441926425
Publisher:	Springer New York
Publication date:	11/19/2010
Series:	Stochastic Modelling and Applied Probability , #60
Edition description:	2009
Pages:	390
Product dimensions:	6.10(w) x 9.25(h) x 0.03(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.

Editorial Reviews

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)

From the Publisher