Limit theorems for multitype epidemics
type: Item
instance of: scholarly article
title: Limit theorems for multitype epidemics
zbMATH Open document ID: 0821.92021
DOI: 10.1016/0304-4149(94)00059-3
author: Håkan Andersson
author: Boualem Djehiche
published in: Stochastic Processes and their Applications
publication date: 1995-05-23T00:00:00Z
review text: The authors studied a local epidemic model -- a spatial version of the classical Kermack-McKendrick model proposed by \textit{D. G. Kendall} [Mathematical models of the spread of infections. (1965)] with a sequence of multitype epidemics. They obtained a law of large numbers and a central limit theorem for the sequence of densities of susceptible and infective individuals as an infinite-dimensional Hilbert space valued stochastic process. In the limit, the fluctuation process turns out to be an infinite-dimensional Ornstein-Uhlenbeck process. The method used is based on Stroock and Varadhans martingale characterization of Hilbert- valued diffusion processes, as developed by \textit{R. A. Holley} and \textit{D. W. Stroock} [Publ. Res. Inst. Math. Sci. 14, 741-788 (1978; Zbl 0412.60065)] and by \textit{M. Métivier} [see C. R. Acad. Sci., Paris, Ser. I 299, 257-260 (1984; Zbl 0564.60049); Ann. Inst. Henri Poincaré, Probab. Stat. 20, 329-348 (1984; Zbl 0549.60041)].
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 757549
zbMATH Keywords: local epidemic model
zbMATH Keywords: Kermack-McKendrick model
zbMATH Keywords: multitype epidemics
zbMATH Keywords: law of large numbers
zbMATH Keywords: central limit theorem
zbMATH Keywords: Hilbert space valued stochastic process
zbMATH Keywords: infinite-dimensional Ornstein-Uhlenbeck process
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)00059-3
OpenAlex ID: W2023725644
cites work: Q4073917
cites work: Q3964422
cites work: Q4134311
cites work: Comparison of stochastic and deterministic models of a linear chemical reaction with diffusion
cites work: Limit theorems for a sequence of nonlinear reaction-diffusion systems
cites work: Q3721531
cites work: Q5509277
cites work: Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
cites work: Law of large numbers and central limit theorem for linear chemical reactions with diffusion
cites work: High density limit theorems for nonlinear chemical reactions with diffusion
cites work: Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
cites work: Q3917278
cites work: Q3904867
cites work: Limit theorems for the motion of a Poisson system of independent Markovian particles with high density
cites work: Semimartingales: A course on stochastic processes
cites work: Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev
cites work: Tightness of probabilities on C([0,1];\(S_ p\)) and D([0,1];\(S_ p\))
cites work: On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
cites work: Semigroups of linear operators and applications to partial differential equations
description: scientific article; zbMATH DE number 757549