Strong and weak order in averaging for SPDEs
Provides rigorous error bounds for averaging in SPDEs, extending known SDE results to infinite-dimensional systems.
This paper proves averaging results for SPDEs with slow and fast time scales, showing strong convergence order 1/2 and weak convergence order 1, matching the SDE case.
We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of the system converges towards the solution of the averaged equation with an order of convergence is 1/2 in a strong sense - approximation of trajectories - and 1 in a weak sense - approximation of laws. These orders turn out to be the same as for the SDE case.