5 research outputs found
On the radius of self-repellent fractional Brownian motion
We study the radius of a self-repellent fractional Brownian motion
taking values in . Our
sharpest result is for , where we find that with high probability,
\begin{equation*}
R_T \asymp T^\nu, \quad \text{with .}
\end{equation*} For , we provide upper and lower bounds for the exponent
, but these bounds do not match
Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise
In this paper, we present a rate of convergence in the uniform norm for the
densities of spatial averages of the solution to the d-dimensional parabolic
Anderson model driven by a Gaussian multiplicative noise, which is white in
time and has a spatial covariance given by the Riesz kernel. The proof is based
on the combination of Malliavin calculus techniques and the Stein's method for
normal approximations