Carsten Hartmann (Brandenburgische Technische Universität Cottbus-Senftenberg)
Complex dynamical systems like molecular systems or stochastic climate systems often involve a variety of different time and length scales. We propose a general framework for coarse graining of such systems when the coefficients in the equations contain parameter uncertainties. Specifically, we consider stochastic differential equations with slow and fast degrees of freedom and uncertain drift or diffusion coefficients. We explain how to derive a coarse-grained (CG) equation for the relevant slow degrees of freedom that represents a worst-case scenario for any given quantity of interest (QoI). The worst-case scenario is formulated using Peng's nonlinear expectation framework that allows to quantify the maximum mean deviation of the QoI from the derived CG approximation. We illustrate the theoretical findings with simple numerical toy examples from stochastic climate modelling.
This is joint work with Hafida Bouanani and Omar Kebiri.