# Analysis of the Rosenblatt process

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 230-257
- ISSN: 1292-8100

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topTudor, Ciprian A.. "Analysis of the Rosenblatt process." ESAIM: Probability and Statistics 12 (2008): 230-257. <http://eudml.org/doc/250393>.

@article{Tudor2008,

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 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.
},

author = {Tudor, Ciprian A.},

journal = {ESAIM: Probability and Statistics},

keywords = {Non Central Limit Theorem; Rosenblatt process;
fractional Brownian motion; stochastic calculus via regularization;
Malliavin calculus; Skorohod integral; non central limit theorem; rosenblatt process; fractional Brownian motion; stochastic calculus regularization; Malliavin calculus},

language = {eng},

month = {1},

pages = {230-257},

publisher = {EDP Sciences},

title = {Analysis of the Rosenblatt process},

url = {http://eudml.org/doc/250393},

volume = {12},

year = {2008},

}

TY - JOUR

AU - Tudor, Ciprian A.

TI - Analysis of the Rosenblatt process

JO - ESAIM: Probability and Statistics

DA - 2008/1//

PB - EDP Sciences

VL - 12

SP - 230

EP - 257

AB -
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.

LA - eng

KW - Non Central Limit Theorem; Rosenblatt process;
fractional Brownian motion; stochastic calculus via regularization;
Malliavin calculus; Skorohod integral; non central limit theorem; rosenblatt process; fractional Brownian motion; stochastic calculus regularization; Malliavin calculus

UR - http://eudml.org/doc/250393

ER -

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