Convergence of mutivalued martingale : Application to multivalued uniform amarts

El-Moustafid Mohamed; Mohammed  El Allali; Fatima Ezzaki; Khalid Tahri

doi:10.5269/bspm.81711

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

Résumé

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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Bibliographies de l'auteur

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.