Edgeworth expansions for slow-fast systems with finite time scale separation

Wouters, J. ORCID: https://orcid.org/0000-0001-5418-7657 and Gottwald, G. A. (2019) Edgeworth expansions for slow-fast systems with finite time scale separation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2223). 20180358. ISSN 1364-5021 doi: 10.1098/rspa.2018.0358

Abstract/Summary

We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is used to asymptotically determine the corrections at any desired order of the time scale parameter ε. The corrections involve integrals over higher-order auto-correlation functions. We develop a diagrammatic representation of the series to control the combinatorial wealth of the asymptotic expansion in ε and provide explicit expressions for the first two orders. At a formal level, the expressions derived are valid in the case when the fast dynamics is stochastic as well as when the fast dynamics is entirely deterministic. We corroborate our analytical results with numerical simulations and show that our method provides an improvement on the classical homogenization limit which is restricted to the limit of infinite time scale separation.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/81424
Identification Number/DOI	10.1098/rspa.2018.0358
Refereed	No
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Nonlinear Sciences - Chaotic Dynamics, Mathematics - Dynamical Systems, Mathematics - Probability
Publisher	Royal Society Publishing
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