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...

We show that randomly stopped partial sums of nonnegative i.i.d. sequences with a geometric stopping variable, inherit some nonparametric class properties defined via the Laplace ordering and that the corresponding converses also hold. Our findings extend earlier results in this direction...

We obtain here the large deviation results for trimmed sums ((r)Sn) of i.i.d. random variables (Xn), with the distribution function belonging to the domain of attraction of a positive stable law. As an application, we establish a law of the iterated logarithm.

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) .