Systems of independent Markov chains (Q1110931)

Consider an infinite system of independent Markov chains as a process on the space of particle configurations. The main results concern possible limiting distributions and equilibrium distribution for these processes. Necessary and sufficient conditions for this convergence are given. If the underlying Markov chain is null recurrent, then every limiting distribution is a Cox process. In the positive recurrent case the limiting distribution is closely related to the invariant probability measure of the Markov chain. Also the transient case is treated.