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Analysis of the Rosenblatt process

Published online by Cambridge University Press:  23 January 2008

Ciprian A. Tudor
Ciprian A. Tudor*
Affiliation:
SAMOS/MATISSE, Centre d'Économie de La Sorbonne, Université de Panthéon-Sorbonne Paris 1, 90, rue de Tolbiac, 75634 Paris cedex 13, France; Ciprian.Tudor@univ-paris1.fr
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Abstract

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears aslimit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process isnon-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral withrespect to the Brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin calculus.

Keywords

Non Central Limit TheoremRosenblatt processfractional Brownian motionstochastic calculus via regularizationMalliavin calculusSkorohod integral

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 230 - 257
Copyright
© EDP Sciences, SMAI, 2008

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