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Birth-death processes with disaster and instantaneous resurrection

Birth-death processes with disaster and instantaneous resurrection

Chen, Anyue, Zhang, Hanjun, Liu, Kai and Rennolls, Keith (2004) Birth-death processes with disaster and instantaneous resurrection. Advances in Applied Probability, 36 (1). pp. 267-292. ISSN 0001-8678 (doi:10.1239/aap/1077134473)

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Abstract

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Item Type: Article
Additional Information: [1] Advances in Applied Probability, published by the Applied Probability Trust.
Uncontrolled Keywords: birth-death process, disaster, instantaneous resurrection, unstable continuous-time Markov chain, existence, uniqueness, recurrence, ergodicity, equilibrium distribution, symmetry, reversibility
Subjects: Q Science > QA Mathematics
Pre-2014 Departments: School of Computing & Mathematical Sciences
School of Computing & Mathematical Sciences > Department of Computer Science
School of Computing & Mathematical Sciences > Statistics & Operational Research Group
Related URLs:
Last Modified: 14 Oct 2016 09:01
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/719

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