The order of convergence in the averaging principle for slow-fast systems of SDE's in Hilbert spaces

Filippo de Feo

Published 2022-03-31Version 1

In this work we are concerned with the study of the strong order of convergence in the averaging principle for slow-fast systems of SDE's in Hilbert spaces when the stochastic perturbations are general Wiener processes, i.e their covariance operators are allowed to be not trace class. In particular we prove that the slow component converges strongly to the averaged one with order of convergence 1/2 which is known to be optimal. Moreover we apply this result to a fully coupled slow-fast stochastic reaction diffusion system where the stochastic perturbation is given by a white noise both in time and space.