Operator-stable laws

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geome...

The Operator Ν-stable Laws

Operator stable laws are the limits of operator normed and centered sums of independent, identically distributed random vectors. The operator ν-stable laws are the analogous limit distributions for randomized sums. In this paper we characterize operator ν-stable laws and their domains of attraction. We also discuss several applications, including the scaling limits of continuous time random wal...

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...

Scaling in stock market data : stable laws

Multiplicative strong unimodality for positive stable laws

It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu [5], the only remaining relevant situation for the multiplicative strong unimodality of stable laws is the one-sided. In this paper, we show that positive α−stable laws are multiplicative strongly ...