Quantitative normal approximations for the stochastic fractional heat equation

Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by general Gaussian multiplicative noise, including cases of space–time white noise and white-colored with spatial covariance given Riesz kernel or bounded integrable function. We show that average over ball radius R converges, as tends to infinity, after suitable renormalization, towards in total variation distance. also provide functional theorem. As such, extend recently proved similar results case Laplacian noise.