Slow-fast systems with fractional environment and dynamics
File(s)
Published version
Author(s)
Li, Xue-Mei
Sieber, Julian
Type
Journal Article
Abstract
We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Hölder norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.
MSC2010: 60G22, 60H10, 37A25.
Keywords: Fractional Brownian motion, averaging, slow-fast system, quenched ergodic theorem, rate of convergence to equilibrium.
MSC2010: 60G22, 60H10, 37A25.
Keywords: Fractional Brownian motion, averaging, slow-fast system, quenched ergodic theorem, rate of convergence to equilibrium.
Date Issued
2022-10-01
Date Acceptance
2022-01-12
Citation
Annals of Applied Probability, 2022, 32 (5), pp.3964-4003
ISSN
1050-5164
Publisher
Institute of Mathematical Statistics
Start Page
3964
End Page
4003
Journal / Book Title
Annals of Applied Probability
Volume
32
Issue
5
Copyright Statement
© 2022 Institute of Mathematical Statistics
Sponsor
Engineering and Physical Sciences Research Council
Engineering & Physical Science Research Council (EPSRC)
EPSRC
Identifier
https://projecteuclid.org/journals/annals-of-applied-probability/volume-32/issue-5/Slow-fast-systems-with-fractional-environment-and-dynamics/10.1214/22-AAP1779.full
Grant Number
EP/V026100/1
EP/V026100/1
EP/S023925/1
Subjects
Statistics & Probability
0102 Applied Mathematics
0104 Statistics
Publication Status
Published
Date Publish Online
2022-10