Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for stochastic dynamical systems

25.11.2019, 12:15  –  Campus Golm, Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Han Cheng Lie (Universität Potsdam)

Global long-term properties of dynamical systems, such as their stationary distribution or rate of mixing, are strongly related to spectral objects of certain operators. These operators, which are known as `transfer operators', describe the evolution of distributions and observables under nonlinear, stochastic dynamics. In this talk, we shall show that for diffusion processes defined by stochastic differential equations (SDEs) in bounded domains with reflecting boundary conditions, these operators depend in a smooth (Frechet) way on the drift coefficient of the SDE. We describe how these smoothness properties carry over to isolated eigenvalues of the transfer operators and the corresponding eigenfunctions.