Some Structure Theorems for the Symmetric Stable Laws

Some Structure Theorems for

A de Bruijn identity for symmetric stable laws

We show how some attractive information–theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat equation. Using this, we derive a version of the de Bruijn identity, allowing us to write the derivative of relative entropy as an inner product of score functio...

M-estimators as GMM for Stable Laws Discretizations

This paper is devoted to "Some Discrete Distributions Generated by Standard Stable Densities" (in short, Discrete Stable Densities). The large-sample properties of M-estimators as obtained by the "Generalized Method of Moments" (GMM) are discussed for such distributions. Some corollaries are proposed. Moreover, using the respective results we demonstrate the large-sample pro...

Functional limit theorems for linear processes in the domain of attraction of stable laws

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable laws.

On the laws of first hitting times of points for one-dimensional symmetric stable Lévy processes

Several aspects of the laws of first hitting times of points are investigated for one-dimensional symmetric stable Lévy processes. Itô’s excursion theory plays a key role in this study.