Weak convergence theorem for a semi-Markovian random walk with delay and Pareto distributed interference of chance

A semi-Markovian random walk with delay and a discrete interference of chance (X(t)) is constructed. The weak convergence theorem is proved for the ergodic distribution of the process X(t) and the limit form of the ergodic distribution is found, when the random variables {ζ_n}, n ≥ 0 have Pareto distribution with parameters (α λ), where the random variables ζ_n describe the discrete interference of chance.