In this paper, we find the conditions under which the expectation of the first coupling moment for two independent, discrete, time-inhomogeneous Markov chains is finite. We consider discrete chains with the phase space {0, 1, . . . }. As the coupling moment, we understand the first moment when both chains visit the zero state at the same time.2010 Mathematics Subject Classification. Primary 60J45; Secondary 60A05, 60K05.

In this paper, we consider two time-inhomogeneous Markov chains X (l) t , l ∈ {1, 2}, with discrete time on a general state space. We assume the existence of some renewal set C and investigate the time of simultaneous renewal, that is, the first positive time when the chains hit the set C simultaneously. The initial distributions for both chains may be arbitrary. Under the condition of stochastic domination and nonlattice condition for both renewal processes, we derive an upper bound for the expectation of the simultaneous renewal time. Such a bound was calculated for two time-inhomogeneous birth-death Markov chains.

No abstract

This paper is devoted to the study of the stability of finite-dimensional distribution of time-inhomogeneous, discrete-time Markov chains on a general state space. The main result of the paper provides an estimate for the absolute difference of finite-dimensional distributions of a given time-inhomogeneous Markov chain and its perturbed version. By perturbation, we mean here small changes in the transition probabilities. Stability estimates are obtained using the coupling method.

In this paper, we consider a nearly critical branching process with immigration. We obtain the rate of convergence in central limit theorem for nearly critical branching processes with immigration.