Articlebronze2008

Analysis of the Rosenblatt process

225 citations0/0 files storedESAIM Probability and Statistics

No readable copy stored yet — this record is metadata only.

Stochastic processes and financial applications Probability and Statistical Research Stochastic processes and statistical mechanics

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.

Citations in this library

Stored only when both papers are in the corpus — 225 citations exist upstream.

References

2006The Malliavin Calculus and Related Topics 1995The Malliavin Calculus and Related Topics 1975Weak convergence to fractional brownian motion and to the rosenblatt process 1999Stochastic Analysis of the Fractional Brownian Motion 1979Convergence of integrated processes of arbitrary Hermite rank 2001Stochastic Calculus with Respect to Gaussian Processes 2002System Control and Rough Paths 2003Fractional Ornstein-Uhlenbeck processes

Cited by

2010Central and non-central limit theorems for weighted power variations of fractional Brownian motion 2007Variations and estimators for the selfsimilarity order through Malliavin calculus 2016Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions 2010Regularization and integral representations of Hermite processes 2014Generalized Hermite processes, discrete chaos and limit theorems 2009Variations and Hurst index estimation for a Rosenblatt process using longer filters

Imported from OpenAlex (CC0) — nothing here is generated.