A System of Denumerably Many Transient Markov Chains

Abstract

If $P$ is a transient Markov chain having the invariant measure $\mu$, and if at time 0 particles are distributed in the state space $\Omega$ according to the Poisson law, with mean $\mu(x)$ at $x$, and these particles are then allowed to move independently of the others according to the law $P$, the system maintains itself in macroscopic equilibrium. In this paper we investigate several phenomena connected with this system.