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Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization.

Authors :
Engel, Maximilian
Gkogkas, Marios Antonios
Kuehn, Christian
Source :
Journal of Statistical Physics; May2021, Vol. 183 Issue 2, p1-34, 34p
Publication Year :
2021

Abstract

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter ε such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with ergodic invariant measure. Convergence of the slow process to the solution of a homogenized stochastic differential equation (SDE) in the limit ε to zero, with explicit formulas for drift and diffusion coefficients, has so far only been obtained for the case that the fast dynamics evolve independently. In this paper we give sufficient conditions for the convergence of the first moments of the slow variable in the coupled case. Our proof is based upon a new method of stochastic regularization and functional-analytical techniques combined via a double limit procedure involving a zero-noise limit as well as considering ε to zero. We also give exact formulas for the drift and diffusion coefficients for the limiting SDE. As a main application of our theory, we study weakly-coupled systems, where the coupling only occurs in lower time scales. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00224715
Volume :
183
Issue :
2
Database :
Complementary Index
Journal :
Journal of Statistical Physics
Publication Type :
Academic Journal
Accession number :
150116871
Full Text :
https://doi.org/10.1007/s10955-021-02765-7