Stationary distribution for birth and death process with one-side bounded jumps

Abstract

In this paper, we study a birth and death process $\{N_t{\}}_{t\ge 0}$ on positive half lattice, which at each discontinuity jumps at most a distance $R\ge 1$ to the right or exactly a distance $1$ to the left. The transitional probabilities at each site are nonhomogeneous. Firstly, sufficient conditions for the recurrence and positive recurrence are presented. Then by the branching structure within random walk with one-side bounded jumps set up in Hong and Wang (2013), the explicit form of the stationary distribution of the process $\{N_t{\}}_{t\ge 0}$ is formulated.

6 pages

References in corpus (2)

• Birth and death process with one-side bounded jumps in random environment
• Tail asymptotic of the stationary distribution for the state dependent (1,R)-reflecting random walk: near critical