Title: Center manifolds for stochastic systems with rough noise

Speaker: Professor Alexandra Neamtu (University of Konstanz, Germany)

Time: February 25, 2022 (Friday) 4:00 PM-- 5:00 PM

Location: Zoom Meeting ID: 962 1231 0117, Password: 834006

(https://uni-bielefeld.zoom.us/j/96212310117?pwd=REIvRDNmd0RpMUhhazhVN3JHaVNXdz09 )

Abstract: Since the breakthrough in rough paths theory for stochastic ordinary differential equations (SDEs), there has been a strong interest in investigating the rough differential equation (RDE) approach and its numerous applications. Rough path techniques can stay closer to deterministic analytical methods and have the potential to transfer many pathwise ordinary differential equation (ODE) techniques more directly to a stochastic setting. However, there are few works that analyze dynamical properties of RDEs and connect the rough path and random dynamical systems approaches. Here we contribute to this aspect and analyze invariant manifolds for RDEs. By means of a suitably discretized Lyapunov-Perron-type method we prove the existence of local center manifolds for such systems. Our method directly works with the RDE and we exploit rough paths estimates to obtain the relevant contraction properties of the Lyapunov-Perron map. This talk is based on a joint work with Christian Kuehn (Technical University of Munich).