Research papers

On conditions for SLLN for martingales with identically distributed increments

A. I. Sakhanenko

Ugra State University, Khanty-Mansiysk, Russia

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.

UDC: 519.214

MSC: 60F15, 60G42

Received December 18, 2007, published December 25, 2007

Language: English

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