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Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization
- Source :
- Journal of Statistical Physics. 183
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $$\varepsilon $$ 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 $$\varepsilon $$ 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 $$\varepsilon $$ 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.
- Subjects :
- 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
Computer Science::Digital Libraries
01 natural sciences
Regularization (mathematics)
Article
Deterministic homogenization
Coupled systems
Diffusion limit
Zero-noise limit
34E13
35J47
37A50
60F17
60H10
Stochastic differential equation
0103 physical sciences
Convergence (routing)
Applied mathematics
Ergodic theory
Limit (mathematics)
0101 mathematics
Mathematical Physics
Mathematics
010102 general mathematics
Statistical and Nonlinear Physics
Coupling (probability)
ddc
Ordinary differential equation
Computer Science::Mathematical Software
010307 mathematical physics
Invariant measure
Subjects
Details
- ISSN :
- 15729613 and 00224715
- Volume :
- 183
- Database :
- OpenAIRE
- Journal :
- Journal of Statistical Physics
- Accession number :
- edsair.doi.dedup.....31f64973ce27e0c254db5f99b4a7474a