Analysis of the Rosenblatt process

Tudor, Ciprian A.

ESAIM: Probability and Statistics, Tome 12 (2008), pp. 230-257.

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.

Classification : 60G12, 60G15, 60H05, 60H07
Mots clés : non central limit theorem, Rosenblatt process, fractional brownian motion, stochastic calculus via regularization, Malliavin calculus, Skorohod integral

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