Exponential inequalities for associated random variables and strong laws of large numbers

摘要

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n~(-1/2) (log log n)~(1/2) (log n) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n~(-1/3) (log n)~(/2/3) and n~(-1/3) (log n)~(5/3), separately.