Ergodic Theorems for Capacities20200106.pdf (333.47 kB)
Download fileErgodicity of invariant capacities
journal contribution
posted on 2020-02-25, 13:22 authored by Chunrong Feng, Panyu Wu, Huaizhong ZhaoIn 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.
Funding
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)
History
School
- Science
Department
- Mathematical Sciences
Published in
Stochastic Processes and their ApplicationsVolume
130Issue
8Pages
5037 - 5059Publisher
ElsevierVersion
- AM (Accepted Manuscript)
Rights holder
© ElsevierPublisher statement
This 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.Acceptance date
2020-02-21Publication date
2020-02-29Copyright date
2020ISSN
0304-4149Publisher version
Language
- en