ON THE NUMBER OF EVENT APPEARANCES IN A MARKOV CHAIN

The paper presents the estimate for the total variation distance between the distribution of the number of appearances of homogeneous disjoint events in a segment of strongly ergodic Markov chain on the finite state space and accompanying Poisson distribution (i.e., Poisson distribution with a parameter equal to the expectation of the random variable under consideration). For this purpose the Chen-Stein method was used. As a result Poisson and normal limit theorems for the number of events appearances are derived. The considered scheme describes the well-known number of runs on consecutive letters, the number of f -recurrent runs, etc., and can be used for describing the properties of distribution of the special form scan statistic.