Amplitude equations for SPDEs driven by fractional additive noise with small hurst parameter

We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise Hurst parameter [Formula: see text]. Close to a change of stability measured small text], we rely on the natural separation time-scales and establish simplified description essential dynamics. Up an error term bounded by power text] depending can approximate solution SPDE in first order SDE, so-called amplitude equation, which describes dominating pattern changing stability. In second approximation is given fast infinite-dimensional Ornstein–Uhlenbeck process. To this aim, need explicit averaging result for integrals driven parameters.