A martingale approach for detecting the drift of a Wiener process

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.