7 papers
Intermittency of geometric Brownian motion on
Sefika Kuzgun, Felix Otto, Christian Wagner
This short note is motivated by a recently discovered connection between a drift-diffusion process in -dimensional Euclidean space with a divergence-free drift sampled from a st…
Time-dependent averages of a critical long-range stochastic heat equation
Sefika Kuzgun, Ran Tao
We study the time-dependent spatial averages of a critical stochastic partial differential equation, namely the stochastic heat equation in dimension with noise white in…
On the radius of self-repellent fractional Brownian motion
Le Chen, Sefika Kuzgun, Carl Mueller +1
We study the radius of a self-repellent fractional Brownian motion taking values in . Our sharpest result is for , whe…
Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise
Sefika Kuzgun, David Nualart
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…
Convergence of Densities of Spatial Averages of Stochastic Heat Equation
Sefika Kuzgun, David Nualart
In this paper, we consider the one-dimensional stochastic heat equation driven by a space time white noise. In two different scenarios: {\it (i)} initial condition and gene…
Feynman-Kac formula for iterated derivatives of the parabolic Anderson model
Sefika Kuzgun, David Nualart
The purpose of this paper is to establish a Feynman-Kac formula for the moments of the iterated Malliavin derivatives of the solution to the parabolic Anderson model in terms of pi…
Rate of Convergence in the Breuer-Major Theorem via Chaos Expansions
Sefika Kuzgun, David Nualart
We show new estimates for the total variation and Wasserstein distances in the framework of the Breuer-Major theorem. The results are based on the combination of Stein's method for…