TY - JOUR A1 - Koltai, Péter A1 - Lie, Han Cheng A1 - Plonka, Martin T1 - Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics JF - Nonlinearity N2 - We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators. Y1 - 2019 U6 - https://doi.org/10.1088/1361-6544/ab1f2a VL - 32 IS - 11 SP - 4232 EP - 4257 ER -