Geodesic
The Structure of a~Stationary Renewal Process
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 134-141

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This article gives the structure of a stationary renewal process with the following property: only a finite number of renewals occurs in any finite time interval with probability 1. 
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G. P. Klimov; L. S. Frank. The Structure of a~Stationary Renewal Process. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 134-141. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a13/