Local limit approximations for Markov population processes
Socoll Sanda N. and Barbour A.D.
Source: J. Appl. Probab.
Volume 46, Number 3
(2009), 690-708.
Abstract
In this paper we are concerned with the equilibrium distribution ∏n of the
nth element in a sequence of continuous-time density-dependent Markov processes
on the integers. Under a (2+α)th moment condition on the jump distributions,
we establish a bound of order O(n-(α+1)/2√logn) on the
difference between the point probabilities of ∏n and those of a translated
Poisson distribution with the same variance. Except for the factor
√logn, 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.
Primary Subjects: 60J75, 62E17
Keywords: Continuous-time Markov jump process; equilibrium distribution; point probabilities; Stein--Chen method; coupling
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279846
Digital Object Identifier: doi:10.1239/jap/1253279846
Zentralblatt MATH identifier:
05611412
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