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Teoriya Veroyatnostei i ee Primeneniya, 1981, Volume 26, Issue 2, Pages 385–391 (Mi tvp2520)  
Short Communications

On the convergence of martingales and geometric properties of Banach spaces

Dang Hung Thang, Nguen Duy Tien

Vietnam, Hanoi
Full-text PDF (453 kB)
Abstract: In this paper we give a condition which implies the almost sure convergence of a class of martingales with values in a uniformly 2-smooth Banach space. This condition is also necessary if martingales take values in a uniformly 2-convex Banach space. These results allow us to characterize the Hilbert space in terms of the almost sure convergence of martingales.
Received: 16.02.1978
English version:
Theory of Probability and its Applications, 1982, Volume 26, Issue 2, Pages 379–385
DOI: https://doi.org/10.1137/1126038
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Dang Hung Thang, Nguen Duy Tien, “On the convergence of martingales and geometric properties of Banach spaces”, Teor. Veroyatnost. i Primenen., 26:2 (1981), 385–391; Theory Probab. Appl., 26:2 (1982), 379–385
Citation in format AMSBIB
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\paper On the convergence of martingales and geometric properties of Banach spaces
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\yr 1981
\vol 26
\issue 2
\pages 385--391
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\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 2
\pages 379--385
\crossref{https://doi.org/10.1137/1126038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981NJ71600013}
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