On multivalued amarts

• Autorzy: Dudek D. , Zięba W.
• Języki publikacji: EN

Abstrakty

EN

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 L^1-bounded B- valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.

Słowa kluczowe

EN

multivalued martingale; amart; almost sure convergence

PL

martyngał wielomiarowy; zbieżność prawie pewna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 93--99
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Dudek D.

• Institute of Mathematics, Maria Curie-Skłodowska University, Pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

autor

Zięba W.

• Institute of Mathematics, Maria Curie-Skłodowska University, Pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

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