Analysis of the Rosenblatt process
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 Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-It\o 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.
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