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Birth-death processes with disaster and instantaneous resurrection

  • Anyue Chen (a1), Hanjun Zhang (a2), Kai Liu (a3) and Keith Rennolls (a1)
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.

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Corresponding author
Postal address: School of Computing and Mathematical Science, University of Greenwich, 30 Park Row, Greenwich, London SE10 9LS, UK.
∗∗ Email address: a.chen@gre.ac.uk
∗∗∗ Postal address: Department of Mathematics, School of Physical Sciences, University of Queensland, QLD 4072, Australia.
∗∗∗∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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