Fundamentals of Stochastic Filtering
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 widespre
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Alan Bain Dan Crisan
Fundamentals of Stochastic Filtering
Stochastic Mechanics Random Media Signal Processing and Image Synthesis Mathematical Economics and Finance
Stochastic Modelling and Applied Probability (Formerly: Applications of Mathematics)
Stochastic Optimization Stochastic Control Stochastic Models in Life Sciences
Edited by
Advisory Board
60 B. Rozovski˘ı G. Grimmett D. Dawson D. Geman I. Karatzas F. Kelly Y. Le Jan B. Øksendal G. Papanicolaou E. Pardoux
For other titles published in this series, go to www.springer.com/series/602
Alan Bain · Dan Crisan
Fundamentals of Stochastic Filtering
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Alan Bain BNP Paribas 10 Harewood Av London NW1 6AA United Kingdom [email protected]
Man aging Editors B. Rozovski˘ı Division of Applied Mathematics 182 George St. Providence, RI 02912 USA [email protected]
Dan Crisan Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2AZ United Kingdom [email protected]
G. Grimmett Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WB UK [email protected]
ISSN: 0172-4568 Stochastic Modelling and Applied Probability ISBN: 978-0-387-76895-3 e-ISBN: 978-0-387-76896-0 DOI 10.1007/978-0-387-76896-0 Library of Congress Control Number: 2008938477 Mathematics Subject Classification (2000): 93E10, 93E11, 60G35, 62M20, 60H15 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com
Preface
Many aspects of phenomena critical to our lives can not be measured directly. Fortunately models of these phenomena, together with more limited observations frequently allow us to make reasonable inferences about the state of the systems that affect us. The process of using partial observations and a stochastic model to make inferences about an evolving system is known as stochastic filtering. The objective of this text is to assist anyone who would like to become familiar with the theory of stochastic filtering, 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 filtering, who wish to gain a better understanding of the underlying theory. Stochastic filtering in continuous
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