This paper studies coupling methods for proving convergence in distribution of (typically Markovian) stochastic processes in continuous time to their stationary distribution. The paper contains: (a) a simple lemma on $\varepsilon$-coupling; (b) conditions for Markov processes to couple in compact sets; (c) new variants of the coupling proof of the renewal theorem; (d) a convergence result for stochastically monotone Markov processes in an ordered Polish space; and (e) a case study of a queue with superposed renewal input. In a companion paper with Foss, similar discussion is given for many-server queues in continuous time.
@article{1177005657,
author = {Asmussen, Soren},
title = {On Coupling and Weak Convergence to Stationarity},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 739-751},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005657}
}
Asmussen, Soren. On Coupling and Weak Convergence to Stationarity. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 739-751. http://gdmltest.u-ga.fr/item/1177005657/