Ergodicity of invariant capacities
journal contributionposted on 2020-02-25, 13:22 authored by Chunrong Feng, Panyu Wu, Huaizhong Zhao
In this paper, we investigate capacity preserving transformations and their ergodicity. We obtain some limit properties under capacity spaces and then give the concept of ergodicity for a capacity preserving transformation. Based on this definition, we give several characterizations of ergodicity. In particular, we obtain a type of Birkhoff’s ergodic theorem and prove that the ergodicity of a transformation with respect to an upper probability is equivalent to a type of strong law of large numbers.
Random Periodicity in Dynamics with Uncertainty : EP/S005293/1
Royal Society Newton Fund (Ref No. NA150344)
National Key R&D Program of China (Ref No. 2018YFA0703900)
National Natural Science Foundation of China (Ref Nos. 11601280, 11971266)
- Mathematical Sciences
Published inStochastic Processes and their Applications
Pages5037 - 5059
- AM (Accepted Manuscript)
Rights holder© Elsevier
Publisher statementThis paper was accepted for publication in the journal Stochastic Processes and their Applications and the definitive published version is available at https://doi.org/10.1016/j.spa.2020.02.010.