Birth-death processes with disaster and instantaneous resurrection
Anyue Chen, Hanjun Zhang, Kai Liu, and Keith Rennolls
Source: Adv. in Appl. Probab. Volume 36, Number 1 (2004), 267-292.
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.
Primary Subjects: 60J27
Secondary Subjects: 60J80
Keywords: Birth-death process; disaster; instantaneous resurrection; unstable continuous-time Markov chain; existence; uniqueness; recurrence; ergodicity; equilibrium distribution; symmetry; reversibility
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1077134473
Mathematical Reviews number (MathSciNet):
MR2035783
Zentralblatt MATH identifier:
1049.60066
Digital Object Identifier: doi:10.1239/aap/1077134473
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