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Weak star convergence of martingales in a dual space

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Castaing C., Ezzaki F., Lavie M., Saadoune M.

Banach Center Publications

2011

tom 92

nr 1

45-73

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.

Ograniczanie wyników

1 Banach Center Publications

1 Castaing C.

1 Ezzaki F.

1 Lavie M.

1 Saadoune M.

1 2011

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Weak star convergence of martingales in a dual space