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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 1, Pages 78–90
(Mi tvp955)
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This article is cited in 3 scientific papers (total 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
Citation:
P. Franken, A. Streller, “Stationary generalized regenerative processes”, Teor. Veroyatnost. i Primenen., 24:1 (1979), 78–90; Theory Probab. Appl., 24:1 (1979), 79–90
Linking options:
https://www.mathnet.ru/eng/tvp955 https://www.mathnet.ru/eng/tvp/v24/i1/p78
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