Stochastic transport by Gaussian noise
Abstract
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain cases represents the equation for the mean value. From this equation we observe a reduced dissipation property for small times and an enhanced diffusion for large times, with respect to delta correlated noise when regularity is higher than the one of Brownian motion, a fact interpreted qualitatively here as a signature of the modified dissipation observed for 2D turbulent fluids due to the inverse cascade. We give results also for the variance of the solution and for a scaling limit of a two-component noise input.
Cite
@article{arxiv.2305.19293,
title = {Stochastic transport by Gaussian noise},
author = {Franco Flandoli and Francesco Russo},
journal= {arXiv preprint arXiv:2305.19293},
year = {2026}
}