On a problem of sequential hypoteses testing

We study a problem of sequential testing of two simple hypotheses. Sufficient conditions for the existence of a decision rule in a given class are obtained. This conditions are formulated in terms of predictable characteristics of local densities corresponding to the hypothetical measures. The extremal property of the rule is proved. It is shown that our decision rule agrees with the known results for problems of sequential hypotheses testing for the mean of a Wiener process [1] and for the drift of a diffusion type process [2].