| Abstract: |
| Stochastic delay differential equations (SDDEs) can be understood as a class of stochastic evolution equations on infinite-dimensional (path) spaces. As observed by S.-E. A. Mohammed in 1986, these equations do not necessarily induce a stochastic flow. Consequently, they do not induce a random dynamical system (RDS) on a deterministic path space.
Together with M. Ghani Varzaneh and M. Scheutzow, we observed that these equations still induce RDS if we allow the spaces themselves to be random. More precisely, we were able to show that SDDEs induce RDS acting on a particular field of Banach spaces. It turns out that these RDS still have a rich structure that, for example, allows one to deduce the existence of invariant manifolds.
In this talk, we explain why it is necessary to study random dynamical systems on fields of Banach spaces when analyzing the dynamics of SDDEs, and discuss our latest results on this topic. |
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