On the strong law of large numbers for ��-mixing and ��-mixing random variables

We consider the classical Kolmogorov condition for strong law of large numbers for sequences of dependent random variables; the so-called ??-mixing and Rademacher?CMenchoff condition for ??-mixing sequences.     

A functional limit theorem for Erdös and Rényi's law of large numbers

Summary We use the theory of large deviations on function spaces to extend Erdös and Rényi's law of large numbers. In particular, we show that with probability 1, the double-indexed set of paths {W _{N, n} } defined by where , {X _i : _i 1} is an iid sequence of random variables, andh(N)=[clogN] is relatively compact; the limit set is given by the set [xI ^*(x)1/c] whereI ^*(x) = ₀ ¹ I(x(t))dt andI is Cramér's rate function.     

对称随机变量序列的Hájek-Rényi型不等式和强大数律

得到了对称随机变量序列的Hájek-Rényi型不等式,并利用它研究了对称随机变量序列的强大数律.