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Ensemble Averaging for Dynamical Systems Under Fast Oscillating Random Boundary Conditions |
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| Authors: | Wei Wang Jian Ren Jinqiao Duan Guowei He |
| Institution: | 1. Department of Mathematics, Nanjing University, Nanjing, P. R. Chinawangweinju@aliyun.com;3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P. R. China;4. Institute for Pure and Applied Mathematics, University of California, Los Angeles, Los Angeles, California, USA;5. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois, USA;6. Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, P. R. China |
| Abstract: | This article is devoted to providing a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable “mixing” conditions on random boundary conditions and on random body forcing. The ensemble averaged model is a nonlinear stochastic partial differential equation, with the deviation process (i.e., the approximation error process) quantified as the solution of a linear stochastic partial differential equation. |
| Keywords: | Multiscale modeling Ensemble averaging Random partial differential equations Stochastic partial differential equations Random boundary conditions Martingale |