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Analysis of the Rosenblatt process

Ciprian A. Tudor — 2008

ESAIM: Probability and Statistics

We analyze which is a selfsimilar process with stationary increments and which appears as limit in the so-called (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.

Central and non-central limit theorems for weighted power variations of fractional brownian motion

Ivan Nourdin;  David Nualart;  Ciprian A. Tudor — 2010

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order ≥2 of the fractional brownian motion with Hurst parameter ∈(0, 1), where is an integer. The central limit holds for 1/2<≤1−1/2, the limit being a conditionally gaussian distribution. If <1/2 we show the convergence in 2 to a limit which only depends on the fractional brownian motion, and if >1−1/2 we show the convergence in 2 to a stochastic integral with...

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