Weak star convergence of martingales in a dual space

Volume 92 / 2011

C. Castaing, F. Ezzaki, M. Lavie, M. Saadoune Banach Center Publications 92 (2011), 45-73 MSC: 28B20, 60G42, 46A17, 54A20. DOI: 10.4064/bc92-0-4

Abstract

In this paper we present various weak star Kuratowski convergence results for multivalued martingales, supermartingales and multivalued mils in the dual of a separable Banach space. We establish several integral representation formulas for convex weak star compact valued multifunctions defined on a Köthe space and derive several existence results of conditional expectation for multivalued Gelfand-integrable multifunctions. Similar convergence results for Gelfand-integrable martingales in the dual space are provided. We also present a new version of Mosco convergence result for unbounded closed convex integrable supermartingales in a separable Banach spaces having the Radon-Nikodym property. New application to the law of large numbers is also presented.

Authors

  • C. CastaingDépartment de Mathématiques
    Université Montpellier II
    34095 Montpellier Cedex 5, France
    e-mail
  • F. EzzakiLaboratoire modélisation et calcul scientifique
    Département de Mathématiques
    Faculté des Sciences et Techniques
    BP 2202, Fès, Maroc
    e-mail
  • M. LavieLaboratoire de Mathématiques appliquées
    Université de Pau et des Pays de L'Adour
    BP 1155, 64013 Pau Cedex, France
    e-mail
  • M. SaadouneDépartement de Mathématiques
    Université Ibnou Zohr
    Lot. Addalha
    B.P. 8106
    Agadir, Maroc
    e-mail

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