Geometric singular perturbation theory applied to stochastic climate models

Geometric singular perturbation theory offers an efficient framework for the study of ordinary differential equations with well-separated time scales. It combines the construction of invariant manifolds, which allow a low-dimensional effective description of the dynamics reduced to slow variables, with a local analysis near bifurcation points. We present extensions of this theory to systems of slow-fast stochastic differential equations, constructing, in particular, neighbourhoods of invariant manifolds in which sample paths concentrate. This approach will be illustrated on a few simple models of the North-Atlantic Thermohaline Circulation. Joint work with Barbara Gentz (WIAS, Berlin).