Stationary Distribution for a Stochastic System of Complexes Interacting Particles

A stochastic system of particles of n different kinds T₁,...,T_n interacting as complexes is considered. A state of the system is a n-dimensional vector а = (α₁,..., α_n) of Nⁿ vector set with nonnegative integer components. This means that there is a group S_α consisting of α₁ particles of the kind T₁,..., and α_n particles of the kind T_n. Sufficient conditions are given for the closed class of states which are achievable from a given state a. Necessary and sufficient conditions are given for a finite closed class of states. A stationary distribution of the Markov process for the closed class is derived and some particular cases - binomial and Poisson distributions are considered. Relation of the found stationary distribution and the microcanonical and canonical distributions has been established.

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