Abstract for the talk on 26.07.2019 (11:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Sebastian Riedel (TU Berlin)
A dynamical systems approach to singular stochastic delay differential equations
26.07.2019, 11:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, A3 01 (Sophus-Lie-SR)
Stochastic delay differential equations (SDDE) are prominent examples of stochastic differential equations on infinite-dimensional spaces which, in general, do not generate a stochastic flow. Consequently, a dynamical theory to study these equations seemed to be impossible for a long time. In this talk, we solve this problem by showing that SDDE indeed induce random dynamical systems on an infinite dimensional fiber bundle. On this structure, we can prove a Multiplicative Ergodic Theorem which yields a spectral theory for linear SDDE. As an application, we can prove a stable manifold theorem for SDDE. Joint work with Mazyar Ghani Varzaneh and Michael Scheutzow (both TU Berlin).