ASYMPTOTIC BEHAVIOR OF JOINT DISTRIBUTION OF THE OVERSHOOT AND THE FIRST PASSAGE TIME OF MARKOV CHAIN FOR THE LEVEL

Анотація

In the paper we prove a theorem on asymptotic behavior of joint  distribution of overshoot and the first passage time of a Markov chain  homogeneous in time for the level and partially homogeneous in the space. Local limit theorem for the first passage time follows from this theorem as a corollary.