A Renewal Model with Randomly Selected Parameters

Abstract

Let $\{\mu_1, \mu_2, \cdots\}$ be chosen from a strictly stationary, ergodic sequence of random variables each with distribution concentrated on $(0, \infty)$. Let $S_n = T_1 + \cdots + T_n$ be a sum of independent random variables where $T_j$ is exponential with mean $\mu_j$. Limiting properties of $S_n$ are considered. More limiting properties are derived under the assumption that $\{\mu_1, \mu_2, \cdots\}$ is strongly mixing and then under the assumption of independence.