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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015 Number 3, Pages 3–11 (Mi vmumm231)

This article is cited 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

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.

UDC: 519.244.5

Received: 14.03.2012


 English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2015, 70:3, 103–110

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