On Multivalued Amarts

• Autorzy: Dorota Dudek , Wiesław Zięba
• 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 L¹-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.

Kategorie tematyczne

• 60F15: Strong theorems
• 60G48: Generalizations of martingales

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 1
• Strony: 93-99

Daty

wydano

2004

Twórcy

autor

Dorota Dudek

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

autor

Wiesław Zięba

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

Identyfikatory

DOI

10.4064/ba52-1-10