Approximation in sequential rules for discrimination of complex hypotheses and their precision in the problem of signal detection from postdetector data (Q1204668)

The problem of sequential testing of composite parametric hypotheses is investigated. It is a generalization of the results for the sequential testing of two simple hypotheses obtained by \textit{V. I. Lotov} [Theory Probab. Appl. 33, No. 2, 276-285 (1988); translation from Teor. Veroyatn. Primen. 33, No. 2, 295-304 (1988; Zbl 0689.62063)] and \textit{D. Siegmund} [J. Roy. Statist. Soc., Ser. B 37, 394-401 (1975; Zbl 0312.62063)]. The case of discrete and continuous time observations with the logarithm of probability ratio being a process with independent increments is considered. Using the expected value of jumps of the logarithm of probability ratio over barriers, exact formulae for the operating- characteristic function and the expected sample size are given. An application of the results to mixtures of Gaussian signals and Gaussian noise is shown.