The Order of Convergence in the Averaging Principle for Slow-Fast Systems of Stochastic Evolution Equations in Hilbert Spaces

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