Local limit approximations for Markov population processes
| dc.creator | Socoll, Sanda N. | |
| dc.creator | Barbour, A. D. | |
| dc.date | 2009-02-05 | |
| dc.date.accessioned | 2026-07-07T12:38:14Z | |
| dc.date.available | 2026-07-07T12:38:14Z | |
| dc.description | The paper is concerned with the equilibrium distribution $Π_n$ of the $n$-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a $(2+\a)$-th moment condition on the jump distributions, we establish a bound of order $O(n^{-(\a+1)/2}\sqrt{\log n})$ on the difference between the point probabilities of $Π_n$ and those of a translated Poisson distribution with the same variance. Except for the factor $\sqrt{\log n}$, the result is as good as could be obtained in the simpler setting of sums of independent integer-valued random variables. Our arguments are based on the Stein-Chen method and coupling. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0902.0886 | |
| dc.identifier | http://arxiv.org/abs/0902.0886 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218684 | |
| dc.subject | Probability | |
| dc.subject | 60J75, 62E17 | |
| dc.title | Local limit approximations for Markov population processes | |
| dc.type | text |