Fundamentals of Stochastic Filtering

1. Auflage. Softcover version of original hardcover Auflage 2009
ISBN: 978-1-4419-2642-5
Verlag: Springer

Buch, Englisch, 390 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 610 g

Reihe: Stochastic Modelling and Applied Probability

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).

Zielgruppe

Research

Autoren/Hrsg.

Crisan, Dan

Bain, Alan

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Technische Wissenschaften Technik Allgemein Mess- und Automatisierungstechnik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.