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

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