Abstract
We study the decay parameter (the rate of convergence of the transition probabilities) of a birth-death process on $\{0,1,...\}$, which we allow to evanesce by escape, via state 0, to an absorbing state -1. Our main results are representations for the decay parameter under four different scenarios, derived from a unified perspective involving Karlin and McGregor’s representation for the transition probabilities of a birth-death process, and the Courant-Fischer theorem on eigenvalues of a symmetric matrix. We also show how the representations readily yield some upper and lower bounds that have appeared in the literature.
Original language | Undefined |
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Pages (from-to) | 278-289 |
Number of pages | 12 |
Journal | Journal of applied probability |
Volume | 52 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- EWI-25938
- MSC-60J80
- MSC-42C05
- Rate of convergence
- IR-95642
- Birth-death process
- Exponential decay
- METIS-312552
- Orthogonal polynomials