Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
article
Various equicontinuity properties for families of Markov operators have been – andstill are – used in the study of existence and uniqueness of invariant probability forthese operators, and of asymptotic stability. We prove a general result on equivalenceof equicontinuity concepts. It allows comparing results in the literature and switchingfrom one view on equicontinuity to another, which is technically convenient in proofs.More precisely, the characterisation is based on a ‘Schur-like property’ for measures: if asequence of finite signed Borel measures on a Polish space is such that it is bounded intotal variation norm and such that for each bounded Lipschitz function the sequence ofintegrals of this function with respect to these measures converges, then the sequenceconverges in dual bounded Lipschitz norm to a measure.
TNO Identifier
946571
ISSN
01677152
Source
Statistics and Probability Letters, 169
Publisher
Elsevier B.V.
Article nr.
108964
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