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Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale

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  • Ezzaki, Fatima
  • Tahri, Khalid

Abstract

In this paper, we prove a new theorem concerning a representation of set valued regular martingales, the proof is based on martingale selectors approach. As applications, various convergence results of set valued martingales are provided.

Suggested Citation

  • Ezzaki, Fatima & Tahri, Khalid, 2019. "Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:2
    DOI: 10.1016/j.spl.2019.06.024
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    References listed on IDEAS

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    1. Choukairi-Dini, Ahmed, 1990. "M-Convergence, et régularité des martingales multivoques: Epi-martingales," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 49-71, April.
    2. Hess, Christian, 1991. "On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 175-201, October.
    3. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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