Distributions of sample quantiles of measurable stochastic processes are important for the purpose of rational pricing of "look-back" options. In this paper we compute the exact tail behavior of the sample quantile distribution for a large class of infinitely divisible stochastic processes with...

We establish zero-one laws for non-homogeneous forms of any finite order in Gaussian, non-Gaussian stable, or, more generally, in type G random variables. The random arguments in the form can be decoupled, totally coupled, or only partially coupled. These zero-one laws are applied to the study...

We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high-frequency data can considerably improve the quality of estimates of extreme movements in...

We describe the exact tail behavior of the solutions to certain nonlinear stochastic differential equations driven by Lévy motions with regularly varying tails and establish existence and uniqueness of solutions to these equations.

Suppose X and Y are independent nonnegative random variables. We study the behavior of P(XYt), as t -- [infinity], when X has a subexponential distribution. Particular attention is given to obtaining sufficient conditions on P(Yt) for XY to have a subexponential distribution. The relationship...

The efficiency of random search algorithms for both deterministic and stochastic optimization problems is considered.

We describe all possibilities for sample path properties of H-self-similar [alpha]-stable processes with stationary increments for all pairs ([alpha], H), completing the picture presented by Kôno and Maejima (1991).