  In this article, a general problem of sequential statistical inference for
general discrete-time stochastic processes is considered. The problem is to
minimize an average sample number given that Bayesian risk due to incorrect
decision does not exceed some given bound. We characterize the form of optimal
sequential stopping rules in this problem. In particular, we have a
characterization of the form of optimal sequential decision procedures when the
Bayesian risk includes both the loss due to incorrect decision and the cost of
observations.
