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On a functional central limit theorem for Markov population processes

Published online by Cambridge University Press:  01 July 2016

Andrew D. Barbour
Andrew D. Barbour*
Affiliation:
University of Cambridge
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Abstract

Let {XN(t)} be a sequence of continuous time Markov population processes on an n-dimensional integer lattice, such that XN has initial state Nx(0) and has a finite number of possible transitions J from any state X: let the transition X → X + J have rate NgJ(N–1X), and let gJ(x) and x (0) be fixed as N varies. The rate of convergence of √N(N–1XN(t) — ζ (t)) to a Gaussian diffusion is investigated, where ζ(t) is the deterministic approximation to N–1XN(t), and a method of deriving higher order asymptotic expansions for its distribution is justified. The methods are applied to two birth and death processes, and to the closed stochastic epidemic.

Keywords

MARKOV POPULATION PROCESSFUNCTIONAL CENTRAL LIMIT THEOREMEPIDEMICCOMPETITION PROCESSBIRTH AND DEATH PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 21 - 39
Copyright
Copyright © Applied Probability Trust 1974 

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References

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