Project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project A9

Dynamics and asymptotic behaviour of stochastic evolution systems


There are two major themes from stochastic evolution systems which form the core of this joint project. On the one hand we analyse stochastic (ordinary or partial) differential equations with delay and work on extensions of results known for systems without delay. Specific topics are an appropriate Fokker-Planck approach, large deviation principles, optimal error estimates for numerical methods, and transition phenomena at stochastic bifurcations. The second theme concerns the specific long-time behaviour of stochastic evolution systems, such as random attractors for quasilinear equations, finite time extinction results and wave propagation in unbounded domains.