On a functional central limit theorem for Markov population processes
- 1 March 1974
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 6 (1) , 21-39
- https://doi.org/10.2307/1426205
Abstract
Let {XN(t)} be a sequence of continuous time Markov population processes on ann-dimensional integer lattice, such thatXNhas initial stateNx(0) and has a finite number of possible transitionsJfrom any stateX: let the transitionX→X + Jhave rateNgJ(N–1X), and letgJ(x) andx(0) be fixed asNvaries. The rate of convergence of √N(N–1XN(t) —ζ(t)) to a Gaussian diffusion is investigated, whereζ(t) is the deterministic approximation toN–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
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