Fundaments of Stochastic Filtering

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Stochastic Mechanics
Random Media
Signal Processing and Image Synthesis
Mathematical Economics and Finance

Stochastic Modelling
and Applied Probability
Applications of Mathematics)

Stochastic Optimization
Stochastic Control
Stochastic Models in Life Sciences

Edited by

Advisory Board

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

Alan Bain · Dan Crisan

Fundamentals of Stochastic


Alan Bain
BNP Paribas
10 Harewood Av
London NW1 6AA
United Kingdom

Man aging Editors
B. Rozovski˘ı
Division of Applied Mathematics
182 George St.
Providence, RI 02912

Dan Crisan
Department of Mathematics
Imperial College London
180 Queen’s Gate
London SW7 2AZ
United Kingdom

G. Grimmett
Centre for Mathematical Sciences
Wilberforce Road
Cambridge CB3 0WB

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
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Printed on acid-free paper


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...
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