Convergence of the sum of reciprocal renewal times (Q919723)
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scientific article; zbMATH DE number 4161828
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of the sum of reciprocal renewal times |
scientific article; zbMATH DE number 4161828 |
Statements
Convergence of the sum of reciprocal renewal times (English)
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1990
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Assume \(\{X_ n\}_ 1^{\infty}\) are i.i.d. and strictly positive. Put \(S_ n=X_ 1+...+X_ n\) for the corresponding renewal points. Then \(\sum^{\infty}_{1}S_ n^{-1}\) converges a.s. iff \([1-E(\exp (- tT_ 1))]^{-1}\) is integrable in [0,1]. This result is useful in a consensus model [cf. \textit{J. E. Cohen}, \textit{J. Hajnal} and \textit{C. M. Newman}, Stochastic Processes Appl. 22, 315-322 (1986; Zbl 0604.60066)].
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renewal theory
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renewal points
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