On stochastic stationarity of renewal processes
- 1 December 1967
- journal article
- Published by International Press of Boston in Arkiv för Matematik
- Vol. 7 (3) , 249-263
- https://doi.org/10.1007/bf02591631
Abstract
We shall consider point systems inR 1 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.Keywords
This publication has 2 references indexed in Scilit:
- Convergence and invariance questions for point systems in R1 under random motionArkiv för Matematik, 1967
- A simple proof for renewal theoremsCommunications on Pure and Applied Mathematics, 1961