This article is cited in 2 papers

Short Communications

Limit theorems for a model of interacting two-types particles generalizing the Bartlett–McKendrick epidemic process

M. Mirzaev, A. N. Startsev

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: he present paper is a continuation of [A. N. Startsev, Theory Probab. Appl., 46 (2002), pp. 431–447] in which limit theorems are established for the number of particles changing their types to the terminal moment of the process given that the initial numbers of particles of both types tend to infinity. Here this problem is solved under the conditions that the initial number of particles having “energy” is fixed. This assumption leads to models more actual for applications, in particular, in epidemiology. A part of the obtained results (Theorems 1 and 2) has been announced in [M. Mirzaev and A. N. Startsev, Proceedings of the International Conference “Advances in Statistical Inferential Methods” (Almaty, 2003), NITS “Fylym,” Almaty, 2003, pp. 81–85].

Keywords: interaction of particles, non-Markovian models, number of particles changing types, limit theorems.

Received: 02.08.2004
Revised: 27.05.2005

DOI: 10.4213/tvp61

 English version: Theory of Probability and its Applications, 2007, 51:2, 362–367

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