On coupling and weak convergence to stationarity. (English) Zbl 0765.60023

How can we prove the convergence of a process \(Z_ t\) to some stationary distribution? The coupling idea suggests the construction of a second dependent process \(Z_ t'\) already with a stationary distribution. Then show \(Z_ t\) and \(Z_ t'\) are asymptotically close in a sufficient sense. The paper gives new insight to this method in different situations like queues, Harris-recurrent Markov processes, renewal theorem and stochastically monotone Markov processes.


60G10 Stationary stochastic processes
60K05 Renewal theory
60J25 Continuous-time Markov processes on general state spaces
60F05 Central limit and other weak theorems
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