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 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...

We show that the Lévy measure of an associated infinitely divisible random vector in d may charge those quadrants of the space where the coordinates have different signs. We describe further certain families of infinitely divisible random vectors for which association does require the Lévy...

Jointly [alpha]-stable random variables with index 0 [alpha] 2 have only finite moments of order less than [alpha], but their conditional moments can be higher than [alpha]. We provide conditions for this to happen and use the existence of the conditional moments to study the regression...

We investigate the tail behavior of the distributions of subadditive functionals of the sample paths of infinitely divisible stochastic processes when the Lévy measure of the process has suitably defined exponentially decreasing tails. It is shown that the probability tails of such functionals...

We study extremes of (generally) skewed stable processes. In particular we find the asymptotic behavior of the distribution function of the order statistics from a (dependent) stable sample. We give necessary conditions for a.s. boundedness of general stable processes. These conditions turn out...

A null recurrent Markov chain is associated with a stationary mixing S[alpha]S process. The resulting process exhibits such strong dependence that its sample covariance grows at a surprising rate which is slower than one would expect based on the fatness of the marginal distribution tails. An...

We characterize the linear and harmonizable fractional stable motions as the self-similar stable processes with stationary increments whose left-equivalent (or right-equivalent) stationary processes are moving averages and harmonizable respectively.

The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional...