Displaying similar documents to “Weak star convergence of martingales in a dual space”

On Multivalued Amarts

Dorota Dudek, Wiesław Zięba (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the...

On multivalued martingales, multimeasures and multivalued Radon-Nikodym property

Mohamed Zohry (2004)

Bollettino dell'Unione Matematica Italiana

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In this paper we prove a representation result for essentially bounded multivalued martingales with nonempty closed convex and bounded values in a real separable Banach space. Then we turn our attention to the interplay between multimeasures and multivalued Riesz representations. Finally, we give the multivalued Radon-Nikodym property.

Convergence theorems for set-valued conditional expectations

Nikolaos S. Papageorgiou (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy’s martingale convergence theorem, while the second involves a nonmonotone sequence of sub σ -fields.