An Asymptotic Estimation for the Distribution of the Minimum Value in Partial Sum Sequence of Stationary Ergodic Markov Chain and Its Application

This paper gives an asymptotic estimation for the distribution of the minimun value in partial sum sequence of a stationary ergodic Markov chain with finite state space and the es timation to describe the asymptotic behaviour of extinction probability in the Atbreya-Karlin BPRE. （i.e. branching process with random environinents.）