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 E[exp(sTij)] of the first-hitting time Tij for any pair of states i and j, as well as asymptotics for E[exp(sTij)] 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.
Original language | English |
---|---|
Pages (from-to) | 594-607 |
Number of pages | 13 |
Journal | Journal of Theoretical Probability |
Volume | 30 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2017 |
Keywords
- Orthogonal polynomials
- Associated polynomials
- Markov’s theorem