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In this paper we establish some limsup theorems and a generalized uniform law of the iterated logarithm (LIL) for the increments of the partial sums of a strictly stationary and asymptotically negatively associated (ANA) sequence of random variables.

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We establish some large increment results for partial sum processes of a dependent stationary Gaussian sequence via estimating upper bounds of large deviation probabilities on suprema of the Gaussian sequence.

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