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Ergodicity of invariant capacities

journal contribution
posted on 25.02.2020 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.

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 Applications

Volume

130

Issue

8

Pages

5037 - 5059

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher 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

21/02/2020

Publication date

2020-02-29

Copyright date

2020

ISSN

0304-4149

Language

en

Depositor

Prof Huaizhong Zhao. Deposit date: 24 February 2020

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