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

Asmussen, Søren

Ann. Appl. Probab. 2, No. 3, 739-751 (1992).

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.

Reviewer: U.Rösler (Göttingen)

MSC:

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

Keywords:

coupling; Harris-recurrent Markov processes; renewal theorem; stochastically monotone Markov processes