A general framework for simulation of fractional fields

Serge Cohen (1) , Céline Lacaux (2) , Michel Ledoux (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IECN - Institut Élie Cartan de Nancy

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, including linear and harmonizable fractional stable fields. Almost sure and $L^r$-norm rates of convergence, relying on asymptotic developments of the deterministic kernels, are presented as a consequence of an approximation result concerning series of symmetric random variables. When the control measure is infinite, normal approximation has to be used as a complement. The general framework is illustrated by simulations of classical fractional fields.

Domaines: Probabilités [math.PR]

Serge Cohen, Céline Lacaux, Michel Ledoux. A general framework for simulation of fractional fields. Stochastic Processes and their Applications, 2008, 118 (9), pp.1489--1517. ⟨hal-00142691⟩