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Strong and weak orders in averaging for SPDEs. (English) Zbl 1266.60112
Author’s abstract: We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scale. 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 0.5 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.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
70K65 Averaging of perturbations for nonlinear problems in mechanics
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