Quick Search:
Browse by:

 News The deadline for the annual report 2015 is January 31st, 2016

Zurich Open Repository and Archive

## Maintenance: Tuesday, 16.2.2015, 06:00-08:00

Maintenance work on various system components of ZORA. During this time there will be a brief unavailability for about 1 hour. Please be patient.

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-23677

# Barbour, A D; Socoll, S (2009). Local limit approximations for Markov population processes. Journal of Applied Probability, 46(3):690-708.

PDF - Registered users only
165kB
View at publisher
 Preview
Accepted Version
PDF
1MB

## Abstract

We are concerned with the equilibrium distribution $\prod _n$ of the $n$th element in a sequence of continuous-time density-dependent Markov processes on the integers. Under a $(2+\alpha )$th moment condition on the jump distributions, we establish a bound of order $O(n^{-(\alpha +1)/2}\sqrt{ \log n})$ on the difference between the point probabilities of $\prod n$ 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.