This article is cited in 3 papers

Stationary generalized regenerative processes

P. Franken, A. Streller

Humboldt University, Berlin, GDR

Abstract: Based on the so-called «inversion formula» from the theory of stochastic point processes, the concept of stationary and synchroneous version of a generalized regenerative process is introduced. Such processes are generated by given strictly stationary sequences of regeneration cycles without any independence assumptions in general. An ergodic theorem and a formula are proved which expresses the stationary distribution of the process as the time average of the process over a regeneration cycle. Some well-known classes of stochastic processes are special cases of the considered model when the cycles form a Markov chain.

Received: 21.02.1977

 English version: Theory of Probability and its Applications, 1979, 24:1, 79–90

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