Weak star convergence of martingales in a dual space

• Autorzy: C. Castaing , F. Ezzaki , M. Lavie , M. Saadoune
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A17: Bornologies and related structures; Mackey convergence, etc.
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 60G42: Martingales with discrete parameter
• 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 45-73

Daty

wydano

2011

Twórcy

autor

C. Castaing

• Départment de Mathématiques, Université Montpellier II, 34095 Montpellier Cedex 5, France

autor

F. Ezzaki

• Laboratoire modélisation et calcul scientifique, Département de Mathématiques, Faculté des Sciences et Techniques, BP 2202, Fès, Maroc

autor

M. Lavie

• Laboratoire de Mathématiques appliquées, Université de Pau et des Pays de L'Adour, BP 1155, 64013 Pau Cedex, France

autor

M. Saadoune

• Département de Mathématiques, Université Ibnou Zohr, Lot. Addalha, B.P. 8106, Agadir, Maroc

Identyfikatory

DOI

10.4064/bc92-0-4