Limit theorems and diffusion approximations for density dependent Markov chains
1976; Springer Nature; Linguagem: Inglês
10.1007/bfb0120765
ISSN2364-8201
Autores Tópico(s)Bayesian Methods and Mixture Models
ResumoOne parameter families of Markov chains X A (t) with infinitesimal parameters given by q k,k+l A =Af(A −1 k,l) k, l ∈Z′ l≠0 are considered. Under appropriate conditions X A (t)/A converges in probability as A→∞ to a solution of the system of ordinary differential equations, \(\dot X = F(X)\)where F(x)=σt lf(x, l). Limit theorems for these families are reviewed including work of Norman, Barbour and the author. A natural diffusion approximation is discussed.Families of this type include the usual epidemic model, models in chemistry, genetics and in many other areas of application.
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