On coupling epoch for renewal times

Abstract: The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes, the coupling method and subsequent estimation of the convergence rate is used. In the presented small publication, we describe a general approach to using the coupling method for regenerative processes - both in the case of a polynomial and an exponential rate of convergence.