arXiv subjects

Meryem Slaoui

Publications and source records attributed to Meryem Slaoui.

3 recordsLinked to original sources

arXiv2019

Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index

We study the convergence in distribution, as $H\to \frac{1}{2}$ and as $H\to 1$, of the integral $\int_{\mathbb{R}} f(u) dZ^{H}(u) $, where $Z ^{H}$ is a Rosenblatt process with self-similarity index $H\in \left( \frac{1}{2}, 1\right) $ and $f$ is a suitable deterministic function. We focus our analysis on the case of the Rosenblatt Ornstein-Uhlenbeck process, which is the solution of the Langevin equation driven by the Rosenblatt process.

math.PR↗

arXiv2019

Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs

We consider the Wiener integral with respect to a $d$-parameter Hermite process with Hurst multi-index ${\bf H}= (H_{1},\ldots, H_{d}) \in \left( \frac{1}{2}, 1\right) ^{d}$ and we analyze the limit behavior in distribution of this object when the components of ${\bf H}$ tend to $1$ and/or $\frac{1}{2}$. As examples, we focus on the solution to the stochastic heat equation with additive Hermite noise and to the Hermite Ornstein-Uhlenbeck process.

math.PR↗

arXiv2019

Generalized $k$-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus

We analyze the generalized $k$-variations for the solution to the wave equation driven by an additive Gaussian noise which behaves as a fractional Brownian with Hurst parameter $H>\frac{1}{2}$ in time and which is white in space. The $k$-variations are defined along {\it filters} of any order $p\geq 1$ and of any length. We show that the sequence of generalized $k$-variation satisfies a Central Limit Theorem when $p> H+\frac{1}{4}$ and we estimate the rate of convergence for it via the Stein-Malliavin calculus. The results are applied to the estimation of the Hurst index. We construct several consistent estimators for $H$ and these estimators are analyzed theoretically and numerically.

math.PR↗