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On a functional central limit theorem for Markov population processes
- Source :
- Advances in Applied Probability; March 1974, Vol. 6 Issue: 1 p21-39, 19p
- Publication Year :
- 1974
-
Abstract
- Let {XN(t)} be a sequence of continuous time Markov population processes on an n-dimensional integer lattice, such that XNhas initial state Nx(0) and has a finite number of possible transitions Jfrom any state X: let the transition X? X + Jhave rate NgJ(Nā1X), and let gJ(x) and x(0) be fixed as Nvaries. The rate of convergence of vN(Nā1XN(t) ā ?(t)) to a Gaussian diffusion is investigated, where ?(t) is the deterministic approximation to Nā1XN(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.
Details
- Language :
- English
- ISSN :
- 00018678 and 14756064
- Volume :
- 6
- Issue :
- 1
- Database :
- Supplemental Index
- Journal :
- Advances in Applied Probability
- Publication Type :
- Periodical
- Accession number :
- ejs40670402
- Full Text :
- https://doi.org/10.1017/S0001867800039690