Abstract
| Original language | Undefined |
|---|---|
| Place of Publication | Enschede |
| Publisher | University of Twente, Department of Applied Mathematics |
| Number of pages | 13 |
| Publication status | Published - Apr 2015 |
Publication series
| Name | Memorandum of the Department of Applied Mathematics |
|---|---|
| No. | 2044 |
| ISSN (Print) | 1874-4850 |
Keywords
- IR-95675
- METIS-312553
- First-hitting time
- EWI-25939
- Orthogonal polynomials
- Associated polynomials
- Markov's Theorem
- MSC-42C05
- MSC-60J80
- Birth-death process
Cite this
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An orthogonal-polynomial approach to first-hitting times of birth-death processes. / van Doorn, Erik A.
Enschede : University of Twente, Department of Applied Mathematics, 2015. 13 p. (Memorandum of the Department of Applied Mathematics; No. 2044).Research output: Book/Report › Report › Other research output
TY - BOOK
T1 - An orthogonal-polynomial approach to first-hitting times of birth-death processes
AU - van Doorn, Erik A.
N1 - The second file is the latest (online first, open access) version.
PY - 2015/4
Y1 - 2015/4
N2 - In a recent paper [J. Theor. Probab. 25 (2012) 950-980] 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 $\mathbb{E}[e^{sT_{ij}}]$ of the first-hitting time $T_{ij}$ for {\em any} pair of states $i$ and $j$, as well as asymptotics for $\mathbb{E}[e^{sT_{ij}}]$ 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 {\em associated polynomials} and {\em Markov's Theorem}.
AB - In a recent paper [J. Theor. Probab. 25 (2012) 950-980] 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 $\mathbb{E}[e^{sT_{ij}}]$ of the first-hitting time $T_{ij}$ for {\em any} pair of states $i$ and $j$, as well as asymptotics for $\mathbb{E}[e^{sT_{ij}}]$ 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 {\em associated polynomials} and {\em Markov's Theorem}.
KW - IR-95675
KW - METIS-312553
KW - First-hitting time
KW - EWI-25939
KW - Orthogonal polynomials
KW - Associated polynomials
KW - Markov's Theorem
KW - MSC-42C05
KW - MSC-60J80
KW - Birth-death process
M3 - Report
T3 - Memorandum of the Department of Applied Mathematics
BT - An orthogonal-polynomial approach to first-hitting times of birth-death processes
PB - University of Twente, Department of Applied Mathematics
CY - Enschede
ER -