Multivariate tempered stable random measures (ISRMs) are constructed and their corresponding space of integrable functions is characterized in terms a quasi-norm utilizing the so-called Rosinski measure law. In special case exponential ISRMs operator-fractional fields presented by moving-average harmonizable representation, respectively.

The first passage time process of a Lévy subordinator with heavy-tailed Lévy measure has long-range dependent paths. The random fluctuations that appear in a natural scheme of summation and time scaling of such stochastic processes are shown to converge weakly. The limit process, which is neither Gaussian nor stable and which does not have the self-similarity property, is possibly of independen...

In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.