An Orthogonal-Polynomial Approach to First-Hitting Times of Birth–Death Processes

Erik A. Doorn ()
Additional contact information
Erik A. Doorn: University of Twente

Journal of Theoretical Probability, 2017, vol. 30, issue 2, 594-607

Abstract: Abstract In a recent paper in this journal, Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor’s classical results on first-hitting times of a birth–death process on the nonnegative integers by establishing a representation for the Laplace transform $${\mathbb {E}}[e^{sT_{ij}}]$$ E [ e s T i j ] of the first-hitting time $$T_{ij}$$ T i j for any pair of states i and j, as well as asymptotics for $${\mathbb {E}}[e^{sT_{ij}}]$$ E [ e s T i j ] when either i or j tends to infinity. It will be shown here that these results may also be obtained by employing tools from the orthogonal-polynomial toolbox used by Karlin and McGregor, in particular associated polynomials and Markov’s theorem.

Keywords: Birth–death process; First-hitting time; Orthogonal polynomials; Associated polynomials; Markov’s theorem; 60J80; 42C05 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-015-0659-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:30:y:2017:i:2:d:10.1007_s10959-015-0659-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-015-0659-z

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().