Aysmptotic results for boundary functionals of renewal-reward process with delay and pareto distribution interference of chanc

Abstract

In this study, a renewal-reward process (X(t)) with a discrete interference of chance is constructed. Under the assumption when the random variables $\zeta_{n}; n=1,2,3$ which describe a discrete interference of chance have pareto distribution with parameters of $(\alpha, \lamda), \alpha >0, \lamda >0$ , the asmptotic expansions for the first four moments of boundary functionals $\tau_{1}, \gamma_{1}, N_{1}$ are obtained, as $E(\zeta_{1}\rightarrow infty$. Finally, the accuracy of the asymptotic expansions examined with Monte Carlo simulation method.