| Abstract: |
| In this talk, we discuss a new approach to deal with the parameterization
problem of small spatial scales by large ones for stochastic
partial differential equations (SPDEs). The approach is variational in nature, and relies
on stochastic parameterizing manifolds, which are random
manifolds aiming to provide---in a mean square sense---approximate small-scale parameterizations. We will highlight a simple semi-analytic approach to determine such manifolds based on backward-forward auxiliary systems. We will then illustrate the approach on low-dimensional closure problems in the context of a stochastically driven Burgers-type equation in presence of small viscosity and linearly unstable modes. The role of path-dependent, non-Markovian coefficients arising in the related closure systems will also be emphasized. This is joint work with Mickael D. Chekroun (UCLA), James C. McWilliams (UCLA) and Shouhong Wang (IUB). |
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