Maximal inequalities with exponential decay under weak dependence conditions.

We establish large deviation inequalities with exponential decay for the maximum of partial sums of subgaussian random variables. Applying our result to acceptable sequences of bounded mean zero random variables, we strengthen a well-known inequality of Hoeffding. As a consequence we prove a bounded law of iterated logarithm for this class of random variables. The obtained method, also allows us to state a strong integrability property for weighted series of negatively dependent random variables. [ABSTRACT FROM AUTHOR]