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Set valued Aumann–Pettis integrable martingale representation theorem and convergence

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Abstract

It is known in the literature that in the RNP Banach space the set valued uniformly integrable martingale is a regular martingale. In this paper by using a selector approach we provide a weaker condition than uniform integrability of a set valued Aumann–Pettis integrable martingale to be a set valued Aumann–Pettis integrable regular martingale. The Converse is also established. As an application of the aforementioned results, a new convergence result of set valued Pettis integrable martingales in Slice topology is provided.

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Acknowledgements

The authors would like to thank the referees for their valuable comments which helped to improve the manuscript.

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Authors and Affiliations

  1. Laboratory of Modeling and Mathematical Structures, Faculty of Sciences and Technologies, University of Sidi Mohamed Ben Abdellah, Fez, Morocco

    M’hamed El-Louh & Fatima Ezzaki

  2. Stochastic and Deterministic Modeling Laboratory, University Mohammed Premier, FSO, Oujda, Morocco

    Khalid Tahri

Authors
  1. M’hamed El-Louh
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  2. Fatima Ezzaki
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  3. Khalid Tahri
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Correspondence to M’hamed El-Louh.

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Communicated by Denny Leung.

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El-Louh, M., Ezzaki, F. & Tahri, K. Set valued Aumann–Pettis integrable martingale representation theorem and convergence. Ann. Funct. Anal. 11, 1236–1256 (2020). https://doi.org/10.1007/s43034-020-00082-w

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  • DOI: https://doi.org/10.1007/s43034-020-00082-w

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