On Stochastic Models and Optimal Methods in the Quickest Detection Problems

This paper is an introduction to the thematic issue devoted to the optimal and asymptotically optimal methods of decision making in problems of the quickest detection of changes of probability characteristics of observed processes (the “disorder” problem), as well as some general problems of the optimal stopping theory on which the decision of these problems is based. This paper's introductory purpose is twofold: on the one hand it gives a general model covering a variate of schemes describing the appearance of disorder, and on the other hand it describes briefly the specific models and general problems concerning the optimal stopping theory which the papers of this issue contain.