Displaying similar documents to “Best possible sufficient conditions for strong law of large numbers for multi-indexed orthogonal random elements.”

On the bounded laws of iterated logarithm in Banach space

Dianliang Deng (2005)

ESAIM: Probability and Statistics

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In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.

On the Brunk-Chung type strong law of large numbers for sequences of blockwise -dependent random variables

Le Van Thanh (2006)

ESAIM: Probability and Statistics

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For a sequence of blockwise -dependent random variables {≥ 1}, conditions are provided under which lim n → ∞ ( ∑ i = 1 n X i ) / b n = 0 almost surely where {≥ 1} is a sequence of positive constants. The results are new even when . As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [ (1987) 709–715], and Gaposhkin [. (1994) 804–812]. The sharpness of the results is illustrated by examples. ...

A note on the almost sure limiting behavior of the maximun of a sequence of partial sums.

André Adler (1988)

Stochastica

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The goal of this paper is to show that, in most strong laws of large numbers, the n partial sum can be replaced with the largest of the first n sums. Moreover it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results apply also to strong laws for Banach valued random elements.