We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized moments when these functions are random variables. We study...

We consider independent random variables {Xn} with a common distribution function F in the domain of attraction of an asymmetric stable law with exponent α≠1, and we prove limit infimum results for subsequences of partial sums of Xn and random sums.

In this paper, we investigate several sample path properties on the increments of (N,d)-Gaussian random fields and also we obtain the law of iterated logarithm for the Gaussian random field, via estimating upper and lower bounds of large deviation probabilities on suprema of the (N,d)- Gaussian...

In this paper, we establish some limit theorems on the combined Csorgo-Révész increments with moduli of continuity for finite dimensional Gaussian random fields under mild conditions, via estimating upper bounds of large deviation probabilities on suprema of the finite dimensional Gaussian...

Let k be a non-negative integer, and let r1, r2,..., rk be non-negative real numbers satisfying r1 + r2 + ... + rk [less-than-or-equals, slant] 1 and ri+1 + ... + rk (k - i)/k for all i = 1,...,k - 1. It is proved that there exists a constant c such that for any X1,X2,...,Xk non-negative i.i.d....

It is an elementary fact that the existence of moments are determined by the tail behavior of the distribution. The converse, however, needs to be discussed. We provide an elementary example that shows random variables with only a few finite moments may have a p.d.f. [latin small letter f with...