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We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005). By one of the inequalities, we obtain the convergence rate  Open image in new window  for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate  Open image in new window  derived by Oliveira (2005) for the above case.

Exponential Inequalities for Positively Associated Random Variables and Applications