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The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation

MPS-RR 2003-16
June 2003




The Wiener Sequential Testing Problem with Finite Horizon

by: Goran Peskir, Pavel V. Gapeev

Abstract

We present an explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.

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This paper has now been published in Stoch. Stoch. Rep. 76, 59--75 (2004)