A general framework for simulation of fractional fields

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Cohen, Serge²  Lacaux, Celine¹  Ledoux, Michel² 

[1] Nancy Univ, CNRS, INRIA, Inst Elie Cartan,UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[2] Univ Toulouse 3, Inst Math, Lab Stat & Probabilites, F-31062 Toulouse, France

关键词: simulation of random fields;    fractional fields;    infinitely divisible distributions;   

DOI  :  10.1016/j.spa.2007.09.008

来源: Elsevier

【 摘 要 】

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. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free