Properties of operators of additive Markov processes. II. (English. Ukrainian original) Zbl 0939.60079

Bratijchuk, M. S.

Theory Probab. Math. Stat. 57, 1-10 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 1-9 (1997).

The author proceeds the investigation which have been done in his previous paper [ibid. 55, 19-28 (1997); resp. ibid. 55, 20-29 (1996; Zbl 0923.60083)], where a representation for the operator \((I-zA(s))^{-1}\) has been obtained. In this paper the author studies properties of components of the factorization of the above mentioned operator for additive Markov processes \((x_{n}, S_{n}),\) where \(x_{n}\) is a countable Markov chain.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60J05	Discrete-time Markov processes on general state spaces
60K15	Markov renewal processes, semi-Markov processes
47A10	Spectrum, resolvent

Keywords:

additive Markov processes; factorization

Citations:

Zbl 0923.60083