Repository: Freie Universität Berlin, Math Department

Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics

Koltai, P. and Lie, Han Cheng and Plonka, M. (2018) Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics. SFB 1114 Preprint in arXiv:1805.06719 . pp. 1-24. (Submitted)

[img]
Preview
PDF
335kB

Official URL: https://arxiv.org/abs/1805.06719

Abstract

We consider Perron-Frobenius and Koopman operators associated to time-inhomogeneous 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 Perron-Frobenius 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

Repository Staff Only: item control page