Open Access
August, 1992 On Coupling and Weak Convergence to Stationarity
Soren Asmussen
Ann. Appl. Probab. 2(3): 739-751 (August, 1992). DOI: 10.1214/aoap/1177005657


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.


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Soren Asmussen. "On Coupling and Weak Convergence to Stationarity." Ann. Appl. Probab. 2 (3) 739 - 751, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0765.60023
MathSciNet: MR1177907
Digital Object Identifier: 10.1214/aoap/1177005657

Primary: 60J25
Secondary: 60F05 , 60K05

Keywords: coupling , Harris recurrence , Markov processes , renewal theory , Stochastic monotonicity

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
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