Fundamentals of Stochastic Filtering

• Filtering Theory.- The Stochastic 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.

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)