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Strong and weak orders in averaging for SPDEs

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  • Bréhier, Charles-Edouard

Abstract

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 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.

Suggested Citation

  • Bréhier, Charles-Edouard, 2012. "Strong and weak orders in averaging for SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2553-2593.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2553-2593
    DOI: 10.1016/j.spa.2012.04.007
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    References listed on IDEAS

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    1. Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.
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