On the distributions of a renewal reward process and it's additive functional (Q1029503)

Summary: In this study, a renewal reward process with a discrete interference of chance \((X(t))\) is constructed and distribution of the process \(X(t)\) is investigated. One-dimensional distribution of the process \(X(t)\) is given by means of the probability characteristics of the renewal processes \(\{T_n\}\) and \(\{S_n\}\). Moreover, one dimensional distribution function of the additive functional \(J_f(t)\) of the process \(X(t)\) is expressed by the probability characteristics of the initial sequences of the random variables \(\{\xi_n\}\) and \(\{\eta_n\}\).