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Iterated invariance principle for slowly mixing dynamical systems
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Galton, Matt and Melbourne, Ian (2022) Iterated invariance principle for slowly mixing dynamical systems. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 58 (2). pp. 1284-1304. doi:10.1214/21-AIHP1190 ISSN 0246-0203.
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Official URL: https://doi.org/10.1214/21-AIHP1190
Abstract
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals. We illustrate this with examples of deterministic fast-slow systems where our iterated invariance principle yields convergence to a stochastic differential equation.
Nous donnons des critères suffisants de type Gordin assurant qu’un principe d’invariance itéré (renforcé) faible est satisfait pour des systèmes dynamiques déterministes. Un tel principe d’invariance est intrinsèquement relié à l’interprétation des intégrales stochastiques. Nous illustrons ceci par des exemples de systèmes lents-rapides déterministes où notre principe d’invariance itéré implique la convergence vers une équation différentielle stochastique.
| Item Type: | Journal Article | ||||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Annales de l'Institut Henri Poincare (B) Probability and Statistics | ||||||||
| Publisher: | Institute of Mathematical Statistics | ||||||||
| ISSN: | 0246-0203 | ||||||||
| Official Date: | May 2022 | ||||||||
| Dates: |
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| Volume: | 58 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 1284-1304 | ||||||||
| DOI: | 10.1214/21-AIHP1190 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Copyright Holders: | Association des Publications de l’Institut Henri Poincaré | ||||||||
| Date of first compliant deposit: | 18 May 2021 | ||||||||
| Date of first compliant Open Access: | 18 May 2022 | ||||||||
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| Open Access Version: |
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