Rates of convergence of stochastically monotone and continuous time Markovmodels

In this paper we give bounds on the total variation distance from convergen ce of a continuous time positive recurrent Markov process on an arbitrary s tate space, based on Foster-Lyapunov drift and minorisation conditions. Con siderably improved bounds are given in the stochastically monotone case, fo r both discrete and continuous time models, even in the absence of a reacha ble minimal element. These results are applied to storage models and to dif fusion processes.