Stability of null-recurrent Markov chains. I: Non-positivity. (English. Ukrainian original) Zbl 0840.60061

Filonov, Yu. P.

Theory Probab. Math. Stat. 48, 135-141 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 191-199 (1993).

Summary: The paper is concerned with stability of nonpositive homogeneous Markov chains with a general state space and perturbed transition operator. The results obtained generalize a number of assertions for discrete random walks from Chapter 2 of T. M. Liggett’s book “Interacting particle systems” (1985; Zbl 0559.60078).

MSC:

60J10

Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

homogeneous Markov chains; perturbation; random walk; stability; nonpositive Markov chains; random walks

Citations:

Zbl 0559.60078