Coupling and convergence of random elements, processes, and regenerative processes

Abstract

The paper starts by proving that a sequence of random elements can be coupled in such a way that the random elements eventually coincide if and only if liminf of their densities is a density. It continues with a survey of some general coupling theory for stochastic processes and applications to wide sense regenerative processes and Palm theory. Finally, a successful coupling and ɛ-coupling of wide sense regenerative processes is constructed without assuming that the inter-regeneration times have finite mean.