Geodesic
On ergodicity of a~system with two types of interacting particles
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 4, pp. 985-993.

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A system with two types of particles placed in $N$ cells is considered. The first type particles arrive at the system in accordance with a Poisson process. There are $V$ particles of the second type in the system, which destroy the first type particles. The ergodicity condition for the Markov chain which describes the behaviour of the system is proved. 
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     author = {L. G. Afanas'eva and E. M. Ginzburg},
     title = {On ergodicity of a~system with two types of interacting particles},
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L. G. Afanas'eva; E. M. Ginzburg. On ergodicity of a~system with two types of interacting particles. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 4, pp. 985-993. http://geodesic.mathdoc.fr/item/FPM_2000_6_4_a2/