Strong law of large numbers and growth rate for a class of random variable sequences

Fazekas and Klesov [Fazekas, I., Klesov, O., 2000. A general approach to the strong law of large numbers. Theory of Probability and its Applications 45, 436-449] established a Hájek-Rényi-type maximal inequality and obtained a strong law of large numbers (SLLN) for the sums of random variables. Hu and Hu [Hu Shuhe, Hu Ming, 2006. A general approach rate to the strong law of large numbers. Statistics and Probability Letters 76, 843-851] obtained the SLLN and the growth rate for a sequence of random variables by using the Hájek-Rényi-type maximal inequality. This paper obtains some new results of the SLLN and growth rate for strongly positive dependent stochastic sequences, PA sequences, ρ̃-mixing sequences, φ̃-mixing sequences and pairwise negatively quadrant dependent sequences.