Law of the logarithm and law of the iterated logarithm for a class of random variables with non-identical distributions

Let {Y-n,n >= 1} be sequence of random variables with EYn = 0. Assume that the Kolmogrov type exponential inequality is satisfied for {Y-xj = -xI{Y-j < -x } + YjI{vertical bar Y-j vertical bar <= x} + xI{Y-j > x}, j >= 1} with any x > 0. In this paper, the law of the logarithm and law of the iterated logarithm for a class of random variables satisfying the Kolmogrov type exponential inequality with non-identical distributions are obtained. The main results not only extend the known results from NA case to a class of random variables satisfying Kolmogrov type exponential inequality, but also weaken the moment assumptions.