Integral equation methods in change-point detection problems

In a standard formulation, a change-point detection (CPD) problem consists in detecting spontaneous changes in the distribution function of sequential random observations, at some unknown points. In many applications, observations of a random process in discrete or continuous time are received sequentially, and, at a certain moment, random or not but unknown, some probabilistic characteristics of this process are changing. An observer should decide as quickly as possible whether change-points occur or not. Besides, the observer should not raise too many ‘false alarms’, that is, make decisions about detecting change-points when they are not presented.