On strong bounds of rate of convergence for regenerative processes

Abstract

We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. For this aim we propose a new modification of the coupling method which we call stationary coupling method. Use of this stationary coupling method improves the classic results about the convergence rate of the distribution of the regenerative process in the case of a heavy tail. Also this method can be applied for obtaining the bounds of the rate of the convergence for the queueing regenerative processes.