On the first-visit-time problem for birth and death processes with catastrophes

2003/07/15 by Antonio Di Crescenzo, A. Di Crescenzo, V. Giorno +7
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #Probability and Risk Models #Statistical Distribution Estimation and Applications #math.PR #msc:60J27 #msc:60J80

paper · pdf · doi:10.48550/arxiv.math/0307206

23 pages, no figures

arxiv created 2003/07/15 · arxiv updated 2009/12/01

Abstract

For a birth-death process subject to catastrophes, defined on the state-space S=\r,r+1,r+2,...\, with r a positive integer or zero, the first-visit time to a state k∈ S is considered and the Laplace transform of its probability density function is determined, use of which is then made to obtain mean and variance. The Laplace transform of the probability density function of the first effective catastrophe occurrence time and its expected value are also obtained. Some extensions to time-non-homogeneous processes are then provided. Finally, certain additional results concerning the determination of the steady-state distribution and the representation of the transition probabilities are worked out, while some applications to particular birth-death processes are shown in the Appendix.

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