Birth-death processes and associated polynomials


Doorn, Erik A. van (2003) Birth-death processes and associated polynomials. Journal of Computational and Applied Mathematics, 153 (1-2). pp. 497-506. ISSN 0377-0427

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Abstract:We consider birth-death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth-death polynomials. The sequence of associated polynomials linked with a sequence of birth-death polynomials and its orthogonalizing measure can be used in the analysis of the underlying birth-death process in several ways. We briefly review the known applications of associated polynomials, which concern transition and first-entrance time probabilities, and establish some new results in this vein. In particular, our findings indicate how the prevalence of recurrence or $\alpha$-recurrence in a birth-death process can be recognized from certain properties of the orthogonalizing measure for the associated polynomials
Item Type:Article
Copyright:© 2003 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Metis ID: 211981