On probabilities of states of a discrete Markov chain with bounded positive jumps. (Russian) Zbl 0631.60066

Lakatosh, L.

Teor. Veroyatn. Mat., Stat., Kiev 37, 92-94 (1987).

A homogeneous Markov chain is considered with discrete time in state space \(\{\) 0,1,...\(\}\), its negative jumps can be arbitrary, the positive jumps are bounded by the constant 2. This chain is characterized by the generating function of transition probabilities for n steps. The conditions of existence of ergodic distributions are investigated and in terms of roots of an equation in the unit circle explicit expressions determining the ergodic probabilites are obtained.

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60G50	Sums of independent random variables; random walks

Keywords:

generating function of transition probabilities; existence of ergodic distributions; ergodic probabilites