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The stochastic filtering problem: a brief historical account

Part of: Stochastic systems and control Stochastic processes Miscellaneous topics - Partial differential equations Inference from stochastic processes General, mathematics and education Stochastic analysis

Published online by Cambridge University Press:  30 March 2016

Dan Crisan
Dan Crisan*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK. Email address: d.crisan@imperial.ac.uk.
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Abstract

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Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this paper is to give a brief historical account of the subject concentrating on the continuous-time framework.

Keywords

Nonlinear filteringKalman-Bucy filterWiener filterstochastic partial differential equation

MSC classification

Primary: 60G35: Signal detection and filtering 93E11: Filtering 62M20: Prediction
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations 60H15: Stochastic partial differential equations 97A30: History of mathematics and mathematics education
Type
Part 2. The 2014 AP lectures
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 13 - 22
Copyright
Copyright © Applied Probability Trust 2014 

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