The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure...

We find a solution of the optimal stopping problem for the case when a reward function is an integer function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial...