Zhengyan, Lin, The Increments of Partial Sums of a De- pendent Sequence When the Moment Generating Functions do not Exist, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 5(4), 1989, pp. 289-296
In the paper. we give the almost sure limiting behaviour of the increments of partial sums of a mixing sequence when the moment generating functions do not exist. The results obtained are close to those for an independent sequence provided that the mixing coefficients tend to zero rapidly enough.