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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2007, Volume 4, Pages 547–552 (Mi semr171)  
Research papers

On conditions for SLLN for martingales with identically distributed increments

A. I. Sakhanenko

Ugra State University, Khanty-Mansiysk, Russia
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Abstract: For any random variable $X$ with $\mathbf E\big[|X|\log(1+|X|)\big]=\infty$ and $\mathbf{E}X=0$ we construct a sequence $\{X_n:n\ge1\}$ of martingale differences which are identically distributed with $X$ and such that the strong law of large numbers does not hold.
Received December 18, 2007, published December 25, 2007
Bibliographic databases:
Document Type: Article
UDC: 519.214
MSC: 60F15, 60G42
Language: English
Citation: A. I. Sakhanenko, “On conditions for SLLN for martingales with identically distributed increments”, Sib. Èlektron. Mat. Izv., 4 (2007), 547–552
Citation in format AMSBIB
\Bibitem{Sak07}
\by A.~I.~Sakhanenko
\paper On conditions for SLLN for martingales with identically distributed increments
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 547--552
\mathnet{http://mi.mathnet.ru/semr171}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2465440}
\zmath{https://zbmath.org/?q=an:1132.60304}
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