Document ESAIM: PS, 2008, Vol. 12, p. 230-257
DOI: 10.1051/ps:2007037
Analysis of the Rosenblatt process
Ciprian A. TudorSAMOS/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
Received March 3, 2007. Accepted June 4, 2007. Published online 23 January 2008
Abstract
We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as
limit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process is
non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with
respect 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.
Mathematics Subject Classification. 60G12, 60G15, 60H05, 60H07
Key words: Non Central Limit Theorem, Rosenblatt process, fractional Brownian motion, stochastic calculus via regularization, Malliavin calculus, Skorohod integral
© EDP Sciences, SMAI 2008