A criterion on asymptotic stability for partially equicontinuous Markov operators. (English) Zbl 1409.60105
Summary: In this paper, we prove a slight, but practically useful, generalisation of a criterion on asymptotic stability for Markov e-chains by T. Szarek [Ann. Probab. 34, No. 5, 1849–1863 (2006; Zbl 1108.60064)], which is based on the so-called lower bound technique, developed by A. Lasota and J. A. Yorke [Random Comput. Dyn. 2, No. 1, 41–77 (1994; Zbl 0804.47033)]. Simultaneously, we present an alternative proof of this theorem using an asymptotic coupling method introduced by M. Hairer. Our main result is illustrated by an application to random iterated function systems, which are not contracting on average.
MSC:
| 60J05 | Discrete-time Markov processes on general state spaces |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 37A25 | Ergodicity, mixing, rates of mixing |
Keywords:
Markov chain; E-property; asymptotic stability; invariant measure; coupling; iterated function systemReferences:
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