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

André Adler (1988)

Stochastica

The goal of this paper is to show that, in most strong laws of large numbers, the nth 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.

A note on the strong consistency of least squares estimates

Joǎo Lita da Silva (2009)

Discussiones Mathematicae Probability and Statistics

The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.

A strong invariance principle for negatively associated random fields

Guang-hui Cai (2011)

Czechoslovak Mathematical Journal

In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite ( 2 + δ ) th moment and the covariance coefficient u ( n ) exponentially decreases to 0 . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.

A version of the law of large numbers

Katusi Fukuyama (2001)

Colloquium Mathematicae

By the method of Rio [10], for a locally square integrable periodic function f, we prove ( f ( μ t x ) + . . . + f ( μ t x ) ) / n 0 1 f for almost every x and t > 0.

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