Geodesic
Final Distribution for Gani Epidemic Markov Processes
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 873-884

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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, Bessel function
Mots-clés : Laplace transform, Laguerre polynomial. 
@article{MZM_2007_82_6_a6,
     author = {A. V. Mastikhin},
     title = {Final {Distribution} for {Gani} {Epidemic} {Markov} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--884},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a6/}
}
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A. V. Mastikhin. Final Distribution for Gani Epidemic Markov Processes. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 873-884. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a6/