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Ergodicity of invariant capacities

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  • Feng, Chunrong
  • Wu, Panyu
  • Zhao, Huaizhong

Abstract

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.

Suggested Citation

  • Feng, Chunrong & Wu, Panyu & Zhao, Huaizhong, 2020. "Ergodicity of invariant capacities," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5037-5059.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:5037-5059
    DOI: 10.1016/j.spa.2020.02.010
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    References listed on IDEAS

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