TY  - JOUR
A1  - Koltai, Peter
A1  - Lie, Han Cheng
A1  - Plonka, Martin
T1  - Frechet 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.
KW  - stochastic differential equations
KW  - transfer operator
KW  - Koopman operator
KW  - Perron-Frobenius operator
KW  - smooth drift dependence
KW  - linear response
KW  - pathwise expectations
Y1  - 2019
U6  - https://doi.org/10.1088/1361-6544/ab1f2a
SN  - 0951-7715
SN  - 1361-6544
VL  - 32
IS  - 11
SP  - 4232
EP  - 4257
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -