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14 december 1967 On stochastic stationarity of renewal processes
Torbjörn Thedéen
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Ark. Mat. 7(3): 249-263 (14 december 1967). DOI: 10.1007/BF02591631


We shall consider point systems in R1 which are stationary renewal distributed. We let the points undergo random translations which are assumed to be independent identically distributed random variables with a non-degenerate distribution function. The translations are also independent of the starting positions. It is shown in theorem 3.1 that the only distribution of the points which is conserved after the random translations is the Poisson one. Finally in section 4 we give a characterization of renewal processes on the positive semiaxis in terms of conditional mean values.


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Torbjörn Thedéen. "On stochastic stationarity of renewal processes." Ark. Mat. 7 (3) 249 - 263, 14 december 1967.


Published: 14 december 1967
First available in Project Euclid: 31 January 2017

zbMATH: 0183.19801
MathSciNet: MR225395
Digital Object Identifier: 10.1007/BF02591631

Rights: 1967 © Almqvist & Wiksell

Vol.7 • No. 3 • 14 december 1967
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