A limit theorem for a Weiss epidemic process

Abstract

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.