Asymptotic expansions for the ergodic moments of a semi-markovian random walk with a generalized delaying barrier

Abstract

In this study, a semi-Markovian random walk process (X(t)) with a generalized delaying barrier is considered and the ergodic theorem for this process is proved under some weak conditions. Then, the exact expressions and asymptotic expansions for the first four ergodic moments of the process X(t) are obtained.