Discrete approximation of stable white noise - Application to spatial linear filtering.

Clément Dombry (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$ and shot noise approximations available on more general spaces. Limit theorems stating the convergence of discrete random noises to stable white noise are proved. These results are then applied to study moving average spatial random fields with heavy-tailed innovations and related limit theorems. A second application deals with discrete approximation for Brownian Lévy motion on the sphere or on the euclidean space.

Mots clés: stable white noise; stable fractional noise; linear filtering; limit theorems

Domaines: Probabilités [math.PR]

Clément Dombry. Discrete approximation of stable white noise - Application to spatial linear filtering.. 2009. ⟨hal-00366634⟩