ASYMPTOTIC OPTIMALITY FOR ONE CLASS OF TRUNCATED SEQUENTIAL-TESTS

Suppose that (x(t),t greater-than-or-equal-to 0) is a stochastic process of the exponential type with [GRAPHICS] where theta epsilon - subset-of (-infinity, infinity) and V(t) is a measure. For testing the hypothesis theta less-than-or-equal-to theta-0 against theta > theta-0, we have found a class of truncated sequential tests with probability of the first kind of error not exceeding alpha, the expected observation time of tests being asymptotically minimal as alpha down 0.