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 toprovide 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 authors areauthorities 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 INDICE: 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 ConditionalDistribution 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.
- ISBN: 978-0-387-76895-3
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 380
- Fecha Publicación: 01/04/2008
- Nº Volúmenes: 1
- Idioma: Inglés