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Series : Stochastic Modelling and Applied Probability

Fundamentals of Stochastic Filtering, 1st Edition

Fundamentals of Stochastic Filtering, 1st Edition
Author
Bain, Alan/ Crisan, Dan 
Publisher
Springer-Verlag 
Publication Date
Nov, 2008 
ISBN
0387768955 or 9780387768953
HARDCOVER 
390 Pages
出版済み 3週間でお届けいたします。
The delivery time takes 3 weeks

¥ 13,262 (tax included)

Description

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).

Contents

Introduction.
The Stochastic Process.
The Filtering Equations.
Uniqueness of the Solution to the Zakai and the Kushner-Stratonovitch Equations.
Other results.
Finite Dimensional Filters.
The Density of the Conditional Distribution of the Signal.
Numerical Methods for Solving the Filtering Problem.
A Continuous Time Particle Filter.
Particle Filters in Discrete Time.
Measure Theory.
Stochastic Analysis.
References.

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