Limit theorems for multitype epidemics
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)].
infinite-dimensional Ornstein-Uhlenbeck process
scientific article; zbMATH DE number 757549
scientific article