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A Limit Theorem for a Weiss Epidemic Process

Part of:Special processesLimit theoremsMarkov processes

Published online by Cambridge University Press:  30 January 2018

A. V. Kalinkin and
A. V. Mastikhin
A. V. Kalinkin*
Affiliation:
Bauman Moscow State Technical University
A. V. Mastikhin*
Affiliation:
Bauman Moscow State Technical University
*
∗ Postal address: Department of Higher Mathematics, Bauman Moscow State Technical University, 2nd Bauman St., 5, 105005 Moscow, Russia.
∗∗∗ Email address: mastikhin@yandex.ru
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Abstract

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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.

Keywords

Markov epidemic processtransition probabilitiesexponential generating functionclosed solutionbranching property

MSC classification

Primary:60F99: None of the above, but in this section60J27: Continuous-time Markov processes on discrete state spaces60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary:60J80: Branching processes (Galton-Watson, birth-and-death, etc.)92D30: Epidemiology

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015, pp. 247 - 257
Copyright
© Applied Probability Trust 

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