Convergence of mutivalued martingale : Application to multivalued uniform amarts

  • El-Moustafid Mohamed Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah
  • Mohammed El Allali Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah
  • Fatima Ezzaki Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah
  • Khalid Tahri
DOI: https://doi.org/10.5269/bspm.81711

Abstract

In this work, we prove a convergence theorem for bounded martingales taking values in a Banach space Y, without requiring Y to have the Radon Nikodym Property. We then extend this result to martingales with values in ccb(Y) (the set of nonempty, convex, closed, and bounded subsets of Y )under several topologies. As applications, we show the convergence of multivalued uniform asymptotic martingales with values in ccb(Y).

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Author Biographies

Mohammed El Allali , Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah

PHD graduate at Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah and author of numerous articles.

Fatima Ezzaki, Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah

Professor of Mathematics at the Faculty of Sciences and Technology of Fez, University Sidi Mohamed Ben Abdellah and author of numerous articles in probability and statistics.

Khalid Tahri

Professor of Mathematics at the Faculty of Science of Oujda, University Mohammed Premier and author of numerous articles.

Published
2026-04-30
Issue
Vol 44 No 16 (2026): Recent Advances in Analysis and Applied Mathematics
Section
Special Issue: Recent Advancements in Analysis and Applied Mathematics

Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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