Stochastic Analysis Seminar – Michela Ottobre (Heriot Watt University)

Model reduction or coarse graining is a central issue in the applied sciences. For example, when dealing with a very high dimensional system one might be interested in finding a lower dimensional dynamics which retains some of the properties of the initial system. Many coarse graining methods are available, and which one to use depends on the specific structure of the system at hand and on the properties one might like to retain. When more than one method is applicable to the same situation a natural question is whether they all produce the same result and, if not, which one “works best”. In this talk we will consider dynamics described by systems of Stochastic Differential Equations and compare the performance of different coarse graining methods which are routinely used in applications, namely averaging methods and closure methods based on the Gyongy approach of mimicking marginals (often referred to as “conditional expectation methods”). We will discuss numerical and theoretical results as well as (large) gaps on the route to full mathematization of some of these approaches.

This is a joint work with Carsten Hartmann (Cottbus) and Hong Duong (Birmingham).