Journal of Applied Probability

The stochastic filtering problem: a brief historical account

Dan Crisan

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 13-22.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528463

Digital Object Identifier
doi:10.1239/jap/1417528463

Mathematical Reviews number (MathSciNet)
MR3317346

Zentralblatt MATH identifier
1325.60057

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 93E11: Filtering [See also 60G35] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60] 97A30: History of mathematics and mathematics education [See also 01-XX]

Keywords
Nonlinear filtering Kalman-Bucy filter Wiener filter stochastic partial differential equation

Citation

Crisan, Dan. The stochastic filtering problem: a brief historical account. J. Appl. Probab. 51A (2014), 13--22. doi:10.1239/jap/1417528463. https://projecteuclid.org/euclid.jap/1417528463


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