Publikation: Amplitude equations for SPDEs driven by fractional additive noise with small hurst parameter
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We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter H∈(0,1). Close to a change of stability measured with a small parameter ε, we rely on the natural separation of time-scales and establish a simplified description of the essential dynamics. Up to an error term bounded by a power of ε depending on the Hurst parameter we can approximate the solution of the SPDE in first order by an SDE, the so-called amplitude equation, which describes the amplitude of the dominating pattern changing stability. In second order the approximation is given by a fast infinite-dimensional Ornstein–Uhlenbeck process. To this aim, we need to establish an explicit averaging result for stochastic integrals driven by rough fractional noise for small Hurst parameters.
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BLÖMKER, Dirk, Alexandra BLESSING-NEAMTU, 2022. Amplitude equations for SPDEs driven by fractional additive noise with small hurst parameter. In: Stochastics and Dynamics. World Scientific Publishing. 2022, 22(3), 2240013. eISSN 0219-4937. Available under: doi: 10.1142/S0219493722400135BibTex
@article{Blomker2022Ampli-57941, year={2022}, doi={10.1142/S0219493722400135}, title={Amplitude equations for SPDEs driven by fractional additive noise with small hurst parameter}, number={3}, volume={22}, journal={Stochastics and Dynamics}, author={Blömker, Dirk and Blessing-Neamtu, Alexandra}, note={Article Number: 2240013} }
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