Concentration estimates for SPDEs driven by fractional Brownian motion

Abstract

The main goal of this work is to provide sample-path estimates for the solution of slowly time-dependent SPDEs perturbed by a cylindrical fractional Brownian motion. Our strategy is similar to the approach by Berglund and Nader for space-time white noise. However, the setting of fractional Brownian motion does not allow us to use any martingale methods. Using instead optimal estimates for the probability that the supremum of a Gaussian process exceeds a certain level, we derive concentration estimates for the solution of the SPDE, provided that the Hurst index $H$ of the fractional Brownian motion satisfies $H>\frac{1}{4}$. As a by-product, we also obtain concentration estimates for one-dimensional fractional SDEs valid for any $H\in (0,1)$.

14 pages. Some minor corrections

References in corpus (7)

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