Stochastic transport by Gaussian noise

Franco Flandoli; Francesco Russo

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arXiv · 2305.19293

Stochastic transport by Gaussian noise

Franco Flandoli·Francesco Russo

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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.

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Franco Flandoli, Francesco Russo. 2023-05-30. Stochastic transport by Gaussian noise. https://arxiv.org/abs/2305.19293

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