Introduction and Summary

Abstract

This study has three goals. The first is the presentation of working tools needed to quantify the behavior of finite Markov chains in discrete and continuous time when the chain has many degrees of freedom. Ergodic state probabilities, ergodic flow rates, ruin probabilities, passage time and regeneration time distributions and their moments are of typical interest. Applications are oriented largely to reliability theory and inventory theory, but the methods apply as well to other branches of applied probability.