Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions

We study the realized power variations for fourth order linearized Kuramoto–Sivashinsky (LKS) SPDEs and their gradient, driven by space–time white noise in one-to-three dimensional spaces, time, have infinite quadratic variation dimension-dependent Gaussian asymptotic distributions. This class was introduced-with Brownian-time-type kernel formulations Allouba a series of articles starting 2006. He proved existence, uniqueness, sharp spatio-temporal Hölder regularity above equations d=1,2,3. use relationship between LKS-SPDEs Houdré–Villaa bifractional Brownian motion (BBM), yielding temporal central limit theorems gradient. underlying explicit kernels spectral/harmonic analysis to prove our results. On one hand, this work builds on recent works delicate general processes stochastic heat equation noise. other it complements Allouba’s earlier