Analysis of the Rosenblatt process

Ciprian A. Tudor

ESAIM: Probability and Statistics (2008)

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

Abstract

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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.

How to cite

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Tudor, 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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