7732
2019
eng
4232
4257
11
32
article
0
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Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics
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