Stochastic parameterizations of deterministic dynamical systems: Theory, applications and challenges

Stochastic parameterizations of deterministic dynamical systems: Theory, applications and challenges.
There is an increased interest in the stochastic parameterization of deterministic dynamical systems whereby a high-dimensional deterministic dynamical system is reduced to a low-dimensional stochastically driven system.
We discuss standard techniques of stochastic model reduction such as homogenization. Recently rigorous results have been obtained justifying this method. The theory relies on an asymptotic limit of infinite time scale separation which is not always satisfied in real world applications. We present a new method to go beyond this asymptotic limit by employing Edgeworth approximations.
This is joint work with Jeroen Wouters.