Let X(t), t[epsilon][0,[infinity]) be a stable subordinator defined on a probability space ([omega], H, P) and let ar,t0, be a non-negative valued function. Under certain conditions on at, it is shown that there exists a function [beta](t) such that Also, iterated logarithm results for...

Let W(t) be a standard Wiener process and let where at is a nondecreasing function of t with 0 < at [less-than-or-equals, slant] t and t-1at nonincreasing. Let (tk) be some increasing sequence diverging to [infinity]. In this paper we study the almost sure behaviour of lim supk-->[infinity][beta]tk sup0[less-than-or-equals, slant]s[less-than-or-equals, slant]atk W(tk+s) - W(tk) .