On identification of distributions for multiple lao hypotheses testing

Applications of information-theoretical methods in mathematical statistics are reflected in the monographs by Kullback [5], Csisz´ar and K¨orner [2], Gutman [3] and others. In [1] Ahlswede and Haroutunian formulated an ensemble of new problems on multiple hypotheses testing for many objects and on identification of hypotheses. The problem of many (L > 2) hypotheses testing on distributions of a finite state Markov chain is studied in [6] via large deviations techniques. In this paper we solve the problem to identification of distributions of many hypotheses for one object by usage of simple homogeneous stationary finite states of Markov chains.