Three-term Asymptotic Expansion for the Moments of the Ergodic Distribution of a Renewal-reward Process with Gamma Distributed Interference of Chancea

Abstract

In this study, a renewal-reward process with a discrete interference of chance ( X(t)) is investigated. We assume that (X-lambda ( t))(t >= 0) is a renewal-reward process with a gamma distributed interference of chance with parameters (alpha, lambda), alpha > 0, lambda > 0. Under the assumption that the process is ergodic, the paper provides for each alpha > 1 the asymptotic expansions for the moments, the skewness (gamma(3)) and kurtosis (gamma(4)) of the process X-lambda, as lambda -> 0.