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Strong laws of large numbers for sequences of blockwise and pairwise m-dependent random variables
by Le Van Thanh

Vol. 33 No. 4 (2005) P.397~P.405

ABSTRACT

In this paper, we introduce the notions of pairwise $m$-dependence and blockwise and pairwise $m$-dependence of random variables $\{X_n, n \ge 1 \}$. For a sequence of blockwise and pairwise $m$-dependent random variables $\{X_n, n \ge 1 \}$, we provide conditions for $\frac {\sum_{j=1}^{n} (X_j - EX_j) }{n^{\frac 1r}} \to 0$ a.s. as $n \to \infty (1 \le r < 2 )$. We also establish the strong law of large numbers for sequences of pairwise $m$-dependent random variables.

KEYWORDS
Pairwise $m$-dependence, blockwise and pairwise $m$-depence, strong law of large numbers, almost sure convergence, stochastically donimated

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F15

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