| Abstract: |
| Stochastic partial differential equations (SPDEs), with bilinear drift and driven by a degenerate additive noise, will be considered. For such equations, we will present new analytic formulas for Markovian as well as non-Markovian parameterizations of the scales lying beyond a cutoff wavenumber. The derivation of these formulas takes place within a variational approach relying on the theory of stochastic parameterizing manifolds whose main tools and concepts will be introduced. The relationships with the ergodic theory of SPDEs will be discussed and applications to closure in the context of ``Burgulence`` will be presented. The role of path-dependent, non-Markovian coefficients arising in the related closure systems will be also discussed. |
|