We investigate the sample path regularity of operator scaling [alpha]-stable random fields. Such fields were introduced in [H. Biermé, M.M. Meerschaert, H.P. Scheffler, Operator scaling stable random fields, Stochastic Process. Appl. 117 (3) (2007) 312-332.] as anisotropic generalizations of...

A scalar valued random field is called operator-scaling if for some dxd matrix E with positive real parts of the eigenvalues and some H0 we have where denotes equality of all finite-dimensional marginal distributions. We present a moving average and a harmonizable representation of stable...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields,...

This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the useful signal are modeled by generalized Gaussian random variables and its noisy part by independent Gaussian variables, we compute a critical thresholding...

If a set of independent, identically distributed random vectors has heavy tails, so that the covariance matrix does not exist, there is no reason to expect that the sample covariance matrix conveys useful information. On the contrary, this paper shows that the eigenvalues and eigenvectors of the...

Continuous time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. When the time between particle jumps has a slowly varying probability tail, the resulting plume disperses at a slowly varying rate. The limiting stochastic...

For data belonging to the domain of normal attraction of nonnormal operator stable laws we present a strongly consistent estimate of the s pectral measure. The cases of a known or unknown exponent are considered.

We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.

A continuous time random walk (CTRW) is a random walk subordinated to a renewal process, used in physics to model anomalous diffusion. Transition densities of CTRW scaling limits solve fractional diffusion equations. This paper develops more general limit theorems, based on triangular arrays,...