On the strong law of large numbers for sequences of random variables without the independence condition |
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Authors: | V. M. Korchevsky |
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Affiliation: | 1.St. Petersburg State University,St. Petersburg,Russia |
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Abstract: | New sufficient conditions for the applicability of the strong law of large numbers to a sequence of dependent random variables X 1, X 2, …, with finite variances are established. No particular type of dependence between the random variables in the sequence is assumed. The statement of the theorem involves the classical condition Σ n ∞ (log2 n)2/n 2 < ∞, which appears in various theorems on the strong law of large numbers for sequences of random variables without the independence condition. |
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