Markov renewal limit theorems. (Ukrainian, English) Zbl 1199.60318

Degtyar’, S. V.

Teor. Jmovirn. Mat. Stat. 76, 31-37 (2007); translation in Theory Probab. Math. Stat. 76, 33-40 (2008).

The author extends some fundamental results of the classical renewal theory to the so-called Markov renewal equation. The Markov renewal theorems are proved for the scheme of series. For more details see V. M. Shurenkov [Ergodic theorems and related problems, Utrecht: VSP (1998; Zbl 0927.60005)], D. Alimov and V. M. Shurenkov [Ukr. Math. J. 42, No. 11, 1283–1288 (1990); translation from Ukr. Mat. Zh. 42, No. 11, 1443-1448 (1990; Zbl 0729.60065)].

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

60K15	Markov renewal processes, semi-Markov processes
60J25	Continuous-time Markov processes on general state spaces

Keywords:

renewal theory; Markov renewal equation; scheme of series

Citations:

Zbl 0927.60005; Zbl 0729.60065