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Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:10.1016/S0304-4149(99)00125-8)

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Abstract

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Item Type: Article
Uncontrolled Keywords: annihilation, catastrophe, equilibrium distribution, existence, Markov branching process, q-matrix, recurrence, resolvent, state-dependent immigration
Subjects: H Social Sciences > HA Statistics
Pre-2014 Departments: School of Computing & Mathematical Sciences
Related URLs:
Last Modified: 14 Oct 2016 09:00
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/376

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