All Questions

Let $\ell \geqslant 1$. Let us consider $(g_n)_{n \in \mathbb{N}}$ identically distributed independent real gaussian variables and real number $(a_{n_1,\dots n_{\ell}})_{(n_1, \dots, n_{\ell}s)\in\...

The classical Gaussian hypercontractivity is stated as following: Suppose $\xi$ is a Gaussian variable and $H_n(\xi)$ is the space of n-th homogeneous Wiener chaos constructed from $\xi$, then for any ...

Recently, I've asked here a question. While trying to find an answer on my own, I found an idea which I now will briefly describe below. I am not familiar enough with the Malliavin calculus, so my ...

Let $W^H$ be a fBm with Hurst parameter $H$ and let $\mathcal{H}$ be its Cameron-Martin space. Then by Girsanov theorem we know that if $\mathbb{P}$ is an fBm measure, it holds that there exists a ...

Given a gaussian process $g := \mathcal{GP}\left(\mu, \Sigma \right)$, where $\mu$ is the mean and $\Sigma$ is the covariance function, I am interested in estimating the mean value $L_m$ of the ...

The time-derivative $\frac{dB_H}{dt}$ of the fractional Brownian motion may be interpreted as a random Schwartz distribution acting on a test function by $$ \left\langle \frac{dB_H}{dt}, f \right\...