Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2015, Number 3, Pages 3–11 (Mi vmumm231)  
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Disorder problem for a Brownian motion on a segment in the case of uniformly distributed moment of disorder

A. A. Socco

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (371 kB) Citations (2)
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Abstract: The paper deals with the quickest detection of the disorder of a Brownian motion on a finite interval. The unknown moment of disorder is assumed to be uniformly distributed on the interval. The Bayesian and absolute criteria are used as optimality tests. The problem is reduced to a classic optimal stopping problem where the optimal stopping time may be obtained as a solution to integral equations. The existence and uniqueness of the solution of integral equations are proved analytically.
Key words: disorder problem, optimal stopping problem, quickest detection, Brownian motion, uniform distribution.
Received: 14.03.2012
English version:
Moscow University Mathematics Bulletin, 2015, Volume 70, Issue 3, Pages 103–110
DOI: https://doi.org/10.3103/S0027132215030018
Bibliographic databases:
Document Type: Article
UDC: 519.244.5
Language: Russian
Citation: A. A. Socco, “Disorder problem for a Brownian motion on a segment in the case of uniformly distributed moment of disorder”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 3, 3–11; Moscow University Mathematics Bulletin, 70:3 (2015), 103–110
Citation in format AMSBIB
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