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.
Keywords: non central limit theorem, Rosenblatt process, fractional brownian motion, stochastic calculus via regularization, Malliavin calculus, Skorohod integral
@article{PS_2008__12__230_0,
author = {Tudor, Ciprian A.},
title = {Analysis of the {Rosenblatt} process},
journal = {ESAIM: Probability and Statistics},
pages = {230--257},
year = {2008},
publisher = {EDP Sciences},
volume = {12},
doi = {10.1051/ps:2007037},
mrnumber = {2374640},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps:2007037/}
}
Tudor, Ciprian A. Analysis of the Rosenblatt process. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 230-257. doi: 10.1051/ps:2007037
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