Fundamentals of Stochastic Filtering

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

Buch, Englisch, Band 60, 390 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 610 g

Reihe: Stochastic Modelling and Applied Probability

Many aspects of phenomena critical to our lives can not be measured directly. Fortunately models of these phenomena, together with more limited obs- vations frequently allow us to make reasonable inferences about the state of the systems that a?ect us. The process of using partial observations and a stochastic model to make inferences about an evolving system is known as stochastic ?ltering. The objective of this text is to assist anyone who would like to become familiar with the theory of stochastic ?ltering, whether graduate student or more experienced scientist. The majority of the fundamental results of the subject are presented using modern methods making them readily available for reference. The book may also be of interest to practitioners of stochastic ?ltering, who wish to gain a better understanding of the underlying theory. Stochastic ?ltering in continuous time relies heavily on measure theory, stochasticprocessesandstochasticcalculus.Whileknowledgeofbasicmeasure theory and probability is assumed, the text is largely self-contained in that the majority of the results needed are stated in two appendices. This should make it easy for the book to be used as a graduate teaching text. With this in mind, each chapter contains a number of exercises, with solutions detailed at the end of the chapter.

Zielgruppe

Research

Autoren/Hrsg.

Crisan, Dan

Bain, Alan

Fachgebiete

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

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.