This article is cited in 8 papers

Final Distribution for Gani Epidemic Markov Processes

A. V. Mastikhin

N. E. Bauman Moscow State Technical University

Abstract: We consider the Kolmogorov equations for the transition probabilities of a three-dimensional Markov process of special form. For a stationary first equation, an exact solution is obtained using the Riemann method. We obtain asymptotics for the expectation and variance of the final distribution and establish a limit theorem.

Keywords: Gani epidemic process, Markov process, transition probabilities, generating function, Laplace transform, Bessel function, Laguerre polynomial.

UDC: 519.21

Received: 10.11.2006
Revised: 17.04.2007

DOI: 10.4213/mzm4186

 English version: Mathematical Notes, 2007, 82:6, 787–797

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