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.
Citation
Frederick Solomon. "A Renewal Model with Randomly Selected Parameters." Ann. Probab. 8 (3) 622 - 629, June, 1980. https://doi.org/10.1214/aop/1176994733
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