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Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
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Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2022) Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 58 (3). pp. 1305-1327. doi:10.1214/21-AIHP1202 ISSN 0246-0203.
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WRAP-deterministic-homogenization-optimal-moment-assumptions-fast-slow-systems-Melbourne-2021.pdf - Accepted Version - Requires a PDF viewer. Download (1518Kb) | Preview |
Official URL: https://doi.org/10.1214/21-AIHP1202
Abstract
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form xk+1=xk+n−1an(xk,yk)+n−1/2bn(xk,yk),yk+1=Tnyk,where the fast dynamics is given by a family Tn of nonuniformly expanding maps. Part 1 builds on our recent work on martingale approximations for families of nonuniformly expanding maps. We prove an iterated weak invariance principle and establish optimal iterated moment bounds for such maps. (The iterated moment bounds are new even for a fixed nonuniformly expanding map T.) The homogenization results are a consequence of this together with parallel developments on rough path theory in Part 2 by Chevyrev, Friz, Korepanov, Melbourne and Zhang.
| 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), Multiscale modeling, 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: | pp. 1305-1327 | ||||||||
| DOI: | 10.1214/21-AIHP1202 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 29 June 2021 | ||||||||
| Date of first compliant Open Access: | 21 July 2022 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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