Optimal detection of changing properties of random sequences. I. Non-successive detection

It is required to detect successively a «disarray» of random sequences in the Bayesian statement of the problem on the assumption that the «disarray» occurs gradually with a probability smaller than a unity. Recurrent relations are provided for the averaged (over the distribution of the «disarray» time) relation of the likelihood and a posteriori probability of a «disarray». With independent observations this statistical data is proved to be non-uniform Markov functions. Examples are provided.