| Issue |
ESAIM: PS
Volume 12, April 2008
|
|
|---|---|---|
| Page(s) | 230 - 257 | |
| DOI | https://doi.org/10.1051/ps:2007037 | |
| Published online | 23 January 2008 | |
Analysis of the Rosenblatt process
SAMOS/MATISSE, Centre d'Économie de
La Sorbonne, Université de Panthéon-Sorbonne Paris 1,
90, rue de Tolbiac, 75634 Paris cedex 13, France; Ciprian.Tudor@univ-paris1.fr
Received:
3
March
2007
Accepted:
4
June
2007
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.
Mathematics Subject Classification: 60G12 / 60G15 / 60H05 / 60H07
Key words: Non Central Limit Theorem / Rosenblatt process / fractional Brownian motion / stochastic calculus via regularization / Malliavin calculus / Skorohod integral
© EDP Sciences, SMAI, 2008
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