Georg Gottwald (University of Sydney, Australia)
The talk is concerned with recent results on statistical properties of deterministic dynamical systems. We will discuss the problem of finding diffusive limits in multi-scale systems. Homogenization has been widely used in stochastic model reduction of slow-fast systems, including geophysical and climate systems for several decades now. The theory relies on an infinite time scale separation. In this talk we present results for the realistic case of finite time scale separation. In particular, we employ Edgeworth expansions as finite size corrections to the central limit theorem and show improved performance of the reduced stochastic models in numerical simulations. We provide several applications of stochastic parametrizations ranging from toy models to Lagrangian convective transport schemes.
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