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A general method to the strong law of large numbers and its applications. (English) Zbl 1153.60019
A method for proving strong laws of large numbers under very general conditions is presented. The crucial condition is a maximal inequality of Hájek-Rényi type providing sufficiently sharp bounds of a maximal tail probability. The obtained results are applied to sums of both positively associated and negatively associated random sequences. The derived rate of convergence is close to the optimal achievable convergence rate for independent random variables.

MSC:
60F15Strong limit theorems
60E15Inequalities in probability theory; stochastic orderings
60G10Stationary processes