Geodesic
Stationary generalized regenerative processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 78-90

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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. 
@article{TVP_1979_24_1_a5,
     author = {P. Franken and A. Streller},
     title = {Stationary generalized regenerative processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {78--90},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a5/}
}
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P. Franken; A. Streller. Stationary generalized regenerative processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 78-90. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a5/