This article is cited in 46 papers

Markov branching processes with interaction

A. V. Kalinkin

N. E. Bauman Moscow State Technical University

Abstract: In the paper we consider Markov processes, with countable set of states, interpreted as systems of particles of several types that interact as complexes for which the result of interaction with a complex of particles does not depend on the presence of other particles in the system. The apparatus of multivariate generating functions is used to find exact closed solutions of the first and second Kolmogorov system of differential equations for the transition probabilities. In our examples analytic methods are used to treat actual transmutation processes of particles in diverse areas of science.

UDC: 515.124.4

MSC: Primary 60J80, 60K35; Secondary 60J25, 60J35, 60G50, 60G10, 92D30, 82C05, 92D25

Received: 21.02.2001

DOI: 10.4213/rm496

 English version: Russian Mathematical Surveys, 2002, 57:2, 241–304

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