Koltai, P. and Lie, Han Cheng and Plonka, M. (2019) Fréchet differentiable drift dependence of PerronFrobenius and Koopman operators for nondeterministic dynamics. https://iopscience.iop.org/article/10.1088/13616544/ab1f2a, 32 (11). pp. 42324257.

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Official URL: https://doi.org/10.1088/13616544/ab1f2a
Abstract
We consider PerronFrobenius and Koopman operators associated to timeinhomogeneous ordinary stochastic differential equations, and establish their Fréchet differentiability with respect to the drift. 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 PerronFrobenius and Koopman operators.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  2259 
Deposited By:  Silvia Hoemke 
Deposited On:  18 Jul 2018 08:03 
Last Modified:  22 Sep 2020 09:30 
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