Koltai, P. and Lie, Han Cheng and Plonka, M. (2018) Fréchet differentiable drift dependence of PerronFrobenius and Koopman operators for nondeterministic dynamics. SFB 1114 Preprint in arXiv:1805.06719 . pp. 124. (Submitted)

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Official URL: https://arxiv.org/abs/1805.06719
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 > Pure 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:  14 Aug 2018 13:58 
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