Analysis of the Rosenblatt process
ESAIM: Probability and Statistics, Volume 12  (2008), p. 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.

DOI : https://doi.org/10.1051/ps:2007037
Classification:  60G12,  60G15,  60H05,  60H07
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},
     publisher = {EDP-Sciences},
     volume = {12},
     year = {2008},
     pages = {230-257},
     doi = {10.1051/ps:2007037},
     mrnumber = {2374640},
     language = {en},
     url = {http://www.numdam.org/item/PS_2008__12__230_0}
}
Tudor, Ciprian A. Analysis of the Rosenblatt process. ESAIM: Probability and Statistics, Volume 12 (2008) , pp. 230-257. doi : 10.1051/ps:2007037. http://www.numdam.org/item/PS_2008__12__230_0/

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