Journal of Applied Probability
- J. Appl. Probab.
- Volume 51A (2014), 13-22.
The stochastic filtering problem: a brief historical account
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.
J. Appl. Probab., Volume 51A (2014), 13-22.
First available in Project Euclid: 2 December 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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