Convergence rate in precise asymptotics for the law of the iterated logarithm

摘要

Let X,X (1) ,X (2) , . . . be a sequence of independent identically distributed random variables satisfying E[X] = 0, E[X (2)] = sigma (2) > 0, and E[|X| (q) ] < a for some q a (2, 3]. Let S (n) = a (k = 1) (n) X (k) , n a (c) 3/4a1. We prove that where (S-n = 0).