Analysis of the Rosenblatt process

Details Analysis of the Rosenblatt process Analysis of the Rosenblatt process

2006-06-23

arxiv.org/abs/math/0606602v1

ESAIM Probability and Statistics 12 (2008) 230-257

Mathematics

Probability

Scientific paper

10.1051/ps:2007037

We analyze {\em the Rosenblatt process} which is a selfsimilar process with stationary increments and which appears as limit in the so-called {\em 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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