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).