Article Dans Une Revue Electronic Communications in Probability Année : 2025

Concentration estimates for SPDEs driven by fractional Brownian motion

Résumé

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 > ¼. As a by-product, we also obtain concentration estimates for one-dimensional fractional SDEs valid for any H ∈ (0,1).

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Dates et versions

hal-04560006 , version 1 (27-04-2024)

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Nils Berglund, Alexandra Blessing. Concentration estimates for SPDEs driven by fractional Brownian motion. Electronic Communications in Probability, 2025, 30 (none), ⟨10.1214/25-ECP664⟩. ⟨hal-04560006⟩
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