Estimation of Spectral Measure of Stable Random Vectors

Autoregressive Gaussian Random Vectors of First Order

Estimation of stable spectral measures

We present two new estimators of a stable spectral measure. One is based on the empirical characteristic function, the other is based on one dimensional projections of the data. We compare these estimators with the Rachev-Xin-Cheng estimator in an empirical study. Their applications in modeling nancial portfolios are also discussed.

On the concentration of measure phenomenon for stable and related random vectors

where m(f(X)) is a median of f(X) and where Φ is the (one–dimensional) standard normal distribution function. The inequality (1) has seen many extensions and to date, most of the conditions under which these developments hold require the existence of finite exponential moments for the underlying vector X . It is thus natural to explore the robustness of this “concentration phenomenon” and to st...

Random Regularization of Brown Spectral Measure

We generalize a recent result of Haagerup; namely we show that a convolution with a standard Gaussian random matrix regularizes the behavior of Fuglede–Kadison determinant and Brown spectral distribution measure. In this way it is possible to establish a connection between limit eigenvalues distributions of a wide class of random matrices and the Brown measure of the corresponding limits.

Concentration of the Spectral Measure for Large Random Matrices with Stable Entries

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value. AMS 2000 Subject Classification: 60E07, 60F10, 15A42, 15A52

Band Copulas as Spectral Measures for Two-dimensional Stable Random Vectors

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.