Transient phenomena for Markov chains and their applications
Abstract
In this paper we consider a family of irreductible, ergodic and aperiodic Markov chains, depending on a parameter e > 0, so that the local drifts have a critical behaviour (in terms of Pakes lemma). The purpose is to analyze the steady state distributions of these chains (in the sense of weak convergence), when e ¯ 0. Under assumptions involving at most the existence of moments of order 2 + g for the jumps, we show that, whenever X (0) is not ergodic, it is possible to caracterize accurately these limit distributions. Connections with the gamma and uniform distributions are revealed.