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Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2
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Chevyrev, Ilya, Friz, Peter, Korepanov, Alexey, Melbourne, Ian and Zhang, Huilin (2022) Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 58 (3). 1328-1350 . doi:10.1214/21-AIHP1203 ISSN 0246-0203.
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WRAP-deterministic-homogenization-under-optimal-moment-assumptions-fast-slow-systems-Part-2-Melbourne-2021.pdf - Accepted Version - Requires a PDF viewer. Download (1008Kb) | Preview |
Official URL: https://doi.org/10.1214/21-AIHP1203
Abstract
We consider deterministic homogenization for discrete-time fast–slow systems of the form
Xk+1=Xk+n−1an(Xk,Yk)+n−1/2bn(Xk,Yk),Yk+1=TnYk
and give conditions under which the dynamics of the slow equations converge weakly to an Itô diffusion X as n→∞. The drift and diffusion coefficients of the limiting stochastic differential equation satisfied by X are given explicitly. This extends the results of Kelly–Melbourne (J. Funct. Anal. 272 (2017) 4063–4102) from the continuous-time case to the discrete-time case. Moreover, our methods (p-variation rough paths) work under optimal moment assumptions.
Combined with parallel developments on martingale approximations for families of nonuniformly expanding maps in Part 1 by Korepanov, Kosloff and Melbourne, we obtain optimal homogenization results when
Tn is such a family of maps.
| Item Type: | Journal Article | ||||||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Homogenization (Differential equations), Discrete-time systems, Stochastic differential equations | ||||||||||||||||||||||||
| Journal or Publication Title: | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques | ||||||||||||||||||||||||
| Publisher: | European Mathematical Society | ||||||||||||||||||||||||
| ISSN: | 0246-0203 | ||||||||||||||||||||||||
| Official Date: | August 2022 | ||||||||||||||||||||||||
| Dates: |
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| Volume: | 58 | ||||||||||||||||||||||||
| Number: | 3 | ||||||||||||||||||||||||
| Page Range: | 1328-1350 | ||||||||||||||||||||||||
| DOI: | 10.1214/21-AIHP1203 | ||||||||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||||||||
| Date of first compliant deposit: | 6 July 2021 | ||||||||||||||||||||||||
| Date of first compliant Open Access: | 21 July 2022 | ||||||||||||||||||||||||
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