ON THE SEMI-MARKOVIAN RANDOM WALK WITH DELAY AND WEIBULL DISTRIBUTED INTERFERENCE OF CHANCE

In this paper, a semi-Markovian random walk with delay and a discrete interference of chance (X (t))is considered. It is assumed that the random variables {ζn} , n ≥ 1 which describe the discrete interference of chance haveWeibull distribution with parameters (α,λ), α 1, λ 0 . Under this assumption, the ergodicity of this process is discussed and the asymptotic expansions with three terms for the first four moments of the ergodic distribution of the process X(t) are derived, when λ → 0. Moreover, the asymptotic expansions for the skewness and kurtosis of the ergodic distribution of the process X(t) are established.