ИСТИНА

In the present talk we discuss two problems regarding the sequential analysis which are closely related to the optimal stopping theory. To be more specific, we present both the sequential hypothesis testing and the quickest detection problems for a Brownian bridge process, both being treated in the Bayesian setup. For the hypothesis testing problem we assume that we observe either a standard Brownian bridge process or the one with a non-zero terminal pinning point what is equivalent to the presence of the drift term. Our natural desire then is to tell apart these two cases as soon as possible with the smallest in some sense penalty. On the contrary, the quickest detection problem treats with a Brownian bridge process which changes its drift term from zero to some non-zero constant at a random time – the so-called disorder time. Our aim here is to raise an alarm as close to the disorder as possible in some appropriate sense. We will see that both problems in question can be reduced to the corresponding optimal stopping problems for time-inhomogeneous Markov processes and then solved. (The work has been fulfilled under Albert Shiryaev’s supervision.)