Point processes induced by stationary symmetric [alpha]-stable (S[alpha]S) processes can have diverse behavior. We distinguish two cases, depending on whether the stationary S[alpha]S process is governed by a dissipative or conservative flow. In the case of dissipative flows, the process is a...

We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold...

Necessary conditions are given for a symmetric [alpha]-stable (S[alpha]S) process, 1 [alpha] 2, to be Markov. These conditions are then applied to find Markov or weakly Markov processes within certain important classes of S[alpha]S processes: time changed Lévy motion, scale mixed Gaussian...

We study the supremum of 'the' standard isonormal linear process L on a subset of a real Hilbert space H. Upper and lower bounds on the probability that supx[epsilon] LX[lambda], [lambda] large, are found. We treat a number of examples. These include the distribution of the maximum of certain...

We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space L[psi] with a function [psi] satisfying the [Delta]2 condition and, as an application, obtain necessary and sufficient conditions for a symmetric...

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show that the rates are very similar to those of an i.i.d....

We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of...

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...

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...