RENEWAL-TYPE BEHAVIOR OF ABSORPTION TIMES IN MARKOV-CHAINS

This paper studies the absorption time of an integer-valued Markov cha in with a lower-triangular transition matrix. The main results concern the asymptotic behavior of the absorption time when the starting poin t tends to infinity (asymptotics of moments and central limit theorem) . They are obtained using stochastic comparison for Markov chains and the classical theorems of renewal theory. Applications to the descript ion of large random chains of partitions and large random ordered part itions are given.