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


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.


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Frederick Solomon. "A Renewal Model with Randomly Selected Parameters." Ann. Probab. 8 (3) 622 - 629, June, 1980.


Published: June, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0434.60088
MathSciNet: MR573299
Digital Object Identifier: 10.1214/aop/1176994733

Primary: 60K05
Secondary: 60J75

Keywords: exponential distribution , jump process , Renewal process

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 3 • June, 1980
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