Sample correlations of infinite variance time series models: An empirical and theoretical study.
Second complément sur le support des lois indéfiniment divisibles
Semi-stable measures
Series of independent vector valued random variables and absolute continuity of seminorms.
Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes.
In this paper we investigate two classes of exponential dispersion models (EDMs) for overdispersed count data with respect to the Poisson distribution. The first is a class of Poisson mixture with positive Tweedie mixing distributions. As an approximation (in terms of unit variance function) of the first, the second is a new class of EDMs characterized by their unit variance functions of the form μ + μp, where p is a real index related to a precise model. These two classes provide some alternatives...
Some properties of exponential integrals of Levy processes and examples.
Some remarks on stable sequences of random variables
Stable laws and domains of attraction in free probability theory.
Statistical estimates of the parameters of stable laws
Stein estimation for infinitely divisible laws
Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.
Stochastic foundations of the universal dielectric response
We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...
Strictly stable distributions on convex cones.
Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of [Book]
Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum distributions with...
Sur la convergence vers la loi de Poisson
Sur la norme de Fourier. III.
Sur le support de certaines lois indéfiniment divisibles dans un espace vectoriel
Sur une extension de la notion de loi semi-stable