A martingale approach for detecting the drift of a Wiener process

Volkert Paulsen

Stochastic Processes and their Applications, 1999, vol. 80, issue 2, 177-191

Abstract: Lerchez (Ann. Statist. 14, 1986b, 1030-1048) considered a sequential Bayes-test problem for the drift of the Wiener process. In the case of a normal prior an o(c)-optimal test could be constructed. In this paper a new martingale approach is presented, which provides an expansion of the Bayes risk for a one-sided SPRT. Relations to the optimal Bayes risk are given, which show the o(c)-optimality for suitable nonnormal priors.

Keywords: Sequential; probability; ratio; test; Bayes; test; Optimal; stopping; Boundary; crossing; Stochastic; integral; Density; process; Wiener; process (search for similar items in EconPapers)
Date: 1999
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