Chen, Anyue and Liu, Kai (2003) Birth-death processes with an instantaneous reflection barrier. Journal of Applied Probability, 40 (1). pp. 163-179. ISSN 0021-9002 (doi:https://doi.org/10.1239/jap/1044476833)

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Abstract

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

Item Type:	Article
Additional Information:	[1] ISSN 0021-9002 (Print), 1475-6072 (Online) [2] Ref: 03/34
Uncontrolled Keywords:	birth-death process, unstable continuous-time Markov chain, existence, uniqueness, ergodicity, equilibrium distribution
Subjects:	H Social Sciences > HA Statistics
Pre-2014 Departments:	School of Computing & Mathematical Sciences
Related URLs:	Publisher Organisation
Last Modified:	14 Oct 2016 09:01
URI:	http://gala.gre.ac.uk/id/eprint/660

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