Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:https://doi.org/10.1080/15326349708807424)

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Abstract

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Item Type:	Article
Uncontrolled Keywords:	annihilation, birth-death process, catastrophe, equilibrium distribution, factorial moments, mass immigration, occupation probabilities, resolvent, uniqueness
Subjects:	H Social Sciences > HA Statistics
Pre-2014 Departments:	School of Computing & Mathematical Sciences
Related URLs:	Organisation
Last Modified:	14 Oct 2016 09:00
URI:	http://gala.gre.ac.uk/id/eprint/370

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