Robust Approximation of the Stochastic Koopman Operator

We analyze the performance of dynamic mode decomposition (DMD)-based approximations stochastic Koopman operator for random dynamical systems where either dynamics or observables are affected by noise. For many DMD algorithms, presence noise can introduce a bias in operator, leading to poor dynamics. In particular, methods using time delayed observables, such as Hankel DMD, biased when random. new, robust algorithm that approximate despite then demonstrate how this be applied which allows us generate Krylov subspace from single observable. This compute realization observable measured over trajectory. test algorithms several examples.