Inequalities for transition probabilities with taboos and their applications

For geometrically ergodic Markov chains explicit estimates are obtained for the accuracy of approximation of transition probabilities with taboos $_Hp^{(t)}(x,B)$ by the variables $(1-\pi(H))^{t-1}\pi(B)$, where $\pi(\,\cdot\,)$ is a stationary distribution. These estimates are used for the proof of limit theorems on the distribution of the moment of first entry of the trajectory of a Markov chain into a given set and on the distribution of the number of states appearing in a segment of the trajectory of a Markov chain a given number of times.
Bibliography: 24 titles.