Markov chains with a finite-component state space. (English. Russian original) Zbl 0699.60059

Filonov, Yu. P.

Theory Probab. Math. Stat. 40, 137-143 (1990); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 115-120 (1989).

Summary: Tests are considered for recurrence, transience, positivity, and nonpositivity of homogeneous Markov chains with a countable set E of communicating states (partitioned into countable subsets \(E_ 0,...,E_{m-1})\) in terms of the average jumps of an arbitrary function defined on E and of the ergodic probabilities of a family of finite Markov chains connected with transitions between the sets \(E_ i\) \((i=0,...,m-1)\).

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60G10	Stationary stochastic processes

Keywords:

recurrence; transience; positivity; Markov chains