"Wavelet expansion of some stable random processes"

JUAN M. MEDINA; BRUNO CERNUSCHI FRÍAS

Tandil

Congreso; “LX Reunión de Comunicaciones Científicas”, de la Unión Matemática Argentina, UMA 2010, Tandil, del 27 de septiembre al 2 de octubre de 2010.; 2010

Unión Matemática Argentina, UMA.

For a symmetric-stable,  random measure M over R, with finite absolutelycontinuous control measure we define a process, using the Riesz fractional integration operator of order , 0 < p < 1. We show that the graph of this process has an adequate Haussdorf dimension and give otherproperties of its local behavior.For this processes, we study the convergence of its wavelet and multi-resolutionexpansions.Under suitableconditions this convergences is also, with probability one.