Ergodic properties of several interacting poisson particles

Abstract

Beginning with independent Markov processes, multiparameter Markov vector processes are constructed. Stopping time vectors are used to permit stopping of the components at different times, and a strong Markov property is proved. Volkonskii's method of random change of time scale is generalized to permit simultaneous changes of time scale. These results are applied to determining the asymptotic distribution of several interacting Poisson particles in terms of the asymptotic distributions of the particles in the absence of any interaction and the speed functions producing the interaction.