Geodesic
On Chernoff’s hypotheses testing problem for the drift of a Brownian motion
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 778-788 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper contains detailed exposition of the results presented in the short communication [M. V. Zhitlukhin and A. A. Muravlev, Russian Math. Surveys, 66 (2011), pp. 1012–1013]. We consider Chernoff’s problem of sequential testing of two hypotheses about the sign of the drift of a Brownian motion under the assumption that it is normally distributed. We obtain an integral equation which characterizes the optimal decision rule and find its solution numerically.
Keywords: Chernoff’s problem; sequential hypotheses testing; optimal stopping problem; integral equations. 
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M. V. Zhitlukhin; A. A. Muravlev. On Chernoff’s hypotheses testing problem for the drift of a Brownian motion. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 778-788. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a9/

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