Limit distribution for a semi-Markovian random walk with Weibull distributed interference of chance

Abstract

In this paper, a semi-Markovian random walk with a discrete interference of chance (X(t)) is considered. In this study, it is assumed that the sequence of random variables {zeta(n)}, n = 1,2, ... , which describes the discrete interference of chance, forms an ergodic Markov chain with the Weibull stationary distribution. Under this assumption, the ergodic theorem for the process X(t) is discussed. Then the weak convergence theorem is proved for the ergodic distribution of the process X(t) and the limit form of the ergodic distribution is derived.