(A) proof of law of the iterated logarithm by using Wang's maximal inequality

Abstract

Wang(1996) studied variations of Kolmogorov``s inequalily. He derived a sequence of maximal inequalities which sharpen Hoeffding``s inquality. In this thesis, we study the law of the iterated logarithm(LIL) in case the random variables have independent, identical standard normal distribution. In proving the above case, Doob``s submartingale inequality is usually employed to obtain the upper bound of LIL. Here we use Wang``s result to obtain the upper bound of LIL and prove LIL without Doob``s submartingale inequality.