 Constructing transient birth–death processes by means of suitable transformationsAntonio Di Crescenzo, Virginia Giorno and Amelia G. Nobile Applied Mathematics and Computation, 2016, vol. 281, issue C, 152-171 Abstract: For a birth–death process N(t) with a reflecting state at 0 we propose a method able to construct a new birth–death process M(t) defined on the same state-space. The birth and death rates of M(t) depend on the rates of N(t) and on the probability law of the process N(t) evaluated at an exponentially distributed random time. Under a suitable assumption we obtain the conditional probabilities, the mean of the process, and the Laplace transforms of the downward first-passage-time densities of M(t). We also discuss the connection between the proposed method and the notion of ν-similarity, as well as a relation between the distribution of M(t) and the steady-state probabilities of N(t) subject to catastrophes governed by a Poisson process. We investigate new processes constructed from (i) a birth–death process with constant rates, and (ii) a linear immigration-death process. Various numerical computations are performed to illustrate the obtained results. Keywords: Conditional probabilities; First-passage time; Catastrophes; ν-similarity; Immigration-birth–death process; Linear immigration-death process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:281:y:2016:i:c:p:152-171 DOI: 10.1016/j.amc.2016.01.058 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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