Equicontinuous Families of Markov Operators in View of Asymptotic Stability

2017/10/06 by Hille, Sander C., Szarek, Tomasz, Ziemlanska, Maria A.
#37A30 #60J05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1710.02352

Abstract

Relation between equicontinuity, the so called e property and stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its support is nonempty satisfies the e property.

Related

• Relation between the eventual continuity and the e-property for Markov-Feller semigroups
• Asymptotic stability for non-equicontinuous Markov semigroups
• Spectral conditions for uniform P-ergodicities of Markov operators on\n abstract states spaces
• Ergodic property of stable-like Markov chains
• A look at perpetuities via asymptotically homogeneous in space Markov chains