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Article

On Chernoff’s hypotheses testing problem about the drift of a Brownian motion

Theory of Probability and Its Applications. 2013. Vol. 57. No. 4. P. 708-717.
Zhitlukhin M., Alexey Muravlev.
Translator: M. Zhitlukhin, А. А. Муравлев.

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.