Abstract
Let {X
N
(t)} be a sequence of continuous time Markov population processes on an n-dimensional integer lattice, such that X
N
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
–1
X), and let gJ
(x) and x (0) be fixed as N varies. The rate of convergence of √N(N
–1
X
N
(t) — ζ (t)) to a Gaussian diffusion is investigated, where ζ(t) is the deterministic approximation to N
–1
XN
(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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
14 articles.
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