Kernel Methods for Stochastic Dynamical Systems with Application to Koopman Eigenfunctions: Feynman-Kac Representations and RKHS Approximation

This research explores the use of kernel methods to analyze stochastic dynamical systems, focusing on their application to Koopman eigenfunctions. It proposes a framework based on Feynman-Kac representations and Reproducing Kernel Hilbert Space (RKHS) approximations. This methodology offers powerful tools for reduced-order modeling, prediction, and control of complex stochastic systems encountered in various engineering and scientific domains, including fluid dynamics and financial markets.