A limit theorem for a Weiss epidemic process. (English) Zbl 1322.60035

Kalinkin, A. V.; Mastikhin, A. V.

J. Appl. Probab. 52, No. 1, 247-257 (2015).

Summary: For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

MSC:

60F99	Limit theorems in probability theory
60J27	Continuous-time Markov processes on discrete state spaces
60J35	Transition functions, generators and resolvents
60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
92D30	Epidemiology

Keywords:

Markov epidemic process; limit theorem; transition probabilities; exponential generating function; Kolmogorov equations; branching property