7732 2019 eng 4232 4257 11 32 article 0 -- -- -- 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. Nonlinearity 10.1088/1361-6544/ab1f2a yes Péter Koltai Erlinda Körnig Han Cheng Lie Martin Plonka Numerical Mathematics Lie, Han MathPlusAA1-1