A Limit Theorem for a Weiss Epidemic Process. (March 2015)

• Record Type: Journal Article
• Authors: Kalinkin, A. V.; Mastikhin, A. V.
• Is Part Of: Journal of applied probability. Volume 52:Number 1(2015)
• Page Start: 247
• Page End: 257
• Publication Date: 2015-03
• Subjects: Markov epidemic process, -- transition probabilities, -- exponential generating function, -- closed solution, -- branching property; 60F99, -- 60J27, -- 60K35, -- 60J80, -- 92D30; 519.2
• DOI: 10.1017/S0021900200012328
• Languages: English
• ISSNs: 0021-9002

Abstract

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.