English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider Perron-Frobenius and Koopman operators associated totime-inhomogeneous ordinary stochastic differential equations, and establishtheir Fr\'{e}chet differentiability with respect to the drift. This resultrelies on a similar differentiability result for pathwise expectations of pathfunctionals of the solution of the stochastic differential equation, which weestablish using Girsanov's formula. We demonstrate the significance of ourresult in the context of dynamical systems and operator theory, by provingcontinuously differentiable drift dependence of the simple eigen- and singularvalues and the corresponding eigen- and singular functions of the stochasticPerron-Frobenius and Koopman operators.

Fr\'echet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics