163 research outputs found
Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process
The purpose of this paper is to estimate the self-similarity index of the
Rosenblatt process by using the Whittle estimator. Via chaos expansion into
multiple stochastic integrals, we establish a non-central limit theorem
satisfied by this estimator. We illustrate our results by numerical
simulations
A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise
We prove a functional non-central limit theorem for jump-diffusions with
periodic coefficients driven by strictly stable Levy-processes with stability
index bigger than one. The limit process turns out to be a strictly stable Levy
process with an averaged jump-measure. Unlike in the situation where the
diffusion is driven by Brownian motion, there is no drift related enhancement
of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit
Analysis of the Rosenblatt process
We analyze {\em the Rosenblatt process} which is a selfsimilar process with
stationary increments and which appears as limit in the so-called {\em Non
Central Limit Theorem} (Dobrushin and Major (1979), Taqqu (1979)). This process
is non-Gaussian and it lives in the second Wiener chaos. We give its
representation as a Wiener-It\^o 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
Wiener integrals with respect to the Hermite process and a Non-Central Limit Theorem
International audienceWe introduce Wiener integrals with respect to the Hermite process and we prove a Non-Central Limit Theorem in which this integral appears as limit. As an example, we study a generalization of the fractional Ornstein-Uhlenbeck process
A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter
By using chaos expansion into multiple stochastic integrals, we make a
wavelet analysis of two self-similar stochastic processes: the fractional
Brownian motion and the Rosenblatt process. We study the asymptotic behavior of
the statistic based on the wavelet coefficients of these processes. Basically,
when applied to a non-Gaussian process (such as the Rosenblatt process) this
statistic satisfies a non-central limit theorem even when we increase the
number of vanishing moments of the wavelet function. We apply our limit
theorems to construct estimators for the self-similarity index and we
illustrate our results by simulations
- …