Superdiffusive limits for deterministic fast–slow dynamical systems

We consider deterministic fast–slow dynamical systems on [Formula: see text] of the form [Formula: see text] where [Formula: see text] . Under certain assumptions we prove convergence of the m-dimensional process [Formula: see text] to the solution of the stochastic differential equation [Formula: s...

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Autores principales: Chevyrev, Ilya, Friz, Peter K., Korepanov, Alexey, Melbourne, Ian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7593331/
https://www.ncbi.nlm.nih.gov/pubmed/33184525
http://dx.doi.org/10.1007/s00440-020-00988-5
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author Chevyrev, Ilya
Friz, Peter K.
Korepanov, Alexey
Melbourne, Ian
author_facet Chevyrev, Ilya
Friz, Peter K.
Korepanov, Alexey
Melbourne, Ian
author_sort Chevyrev, Ilya
collection PubMed
description We consider deterministic fast–slow dynamical systems on [Formula: see text] of the form [Formula: see text] where [Formula: see text] . Under certain assumptions we prove convergence of the m-dimensional process [Formula: see text] to the solution of the stochastic differential equation [Formula: see text] where [Formula: see text] is an [Formula: see text] -stable Lévy process and [Formula: see text] indicates that the stochastic integral is in the Marcus sense. In addition, we show that our assumptions are satisfied for intermittent maps f of Pomeau–Manneville type.
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spelling pubmed-75933312020-11-10 Superdiffusive limits for deterministic fast–slow dynamical systems Chevyrev, Ilya Friz, Peter K. Korepanov, Alexey Melbourne, Ian Probab Theory Relat Fields Article We consider deterministic fast–slow dynamical systems on [Formula: see text] of the form [Formula: see text] where [Formula: see text] . Under certain assumptions we prove convergence of the m-dimensional process [Formula: see text] to the solution of the stochastic differential equation [Formula: see text] where [Formula: see text] is an [Formula: see text] -stable Lévy process and [Formula: see text] indicates that the stochastic integral is in the Marcus sense. In addition, we show that our assumptions are satisfied for intermittent maps f of Pomeau–Manneville type. Springer Berlin Heidelberg 2020-07-16 2020 /pmc/articles/PMC7593331/ /pubmed/33184525 http://dx.doi.org/10.1007/s00440-020-00988-5 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Chevyrev, Ilya
Friz, Peter K.
Korepanov, Alexey
Melbourne, Ian
Superdiffusive limits for deterministic fast–slow dynamical systems
title Superdiffusive limits for deterministic fast–slow dynamical systems
title_full Superdiffusive limits for deterministic fast–slow dynamical systems
title_fullStr Superdiffusive limits for deterministic fast–slow dynamical systems
title_full_unstemmed Superdiffusive limits for deterministic fast–slow dynamical systems
title_short Superdiffusive limits for deterministic fast–slow dynamical systems
title_sort superdiffusive limits for deterministic fast–slow dynamical systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7593331/
https://www.ncbi.nlm.nih.gov/pubmed/33184525
http://dx.doi.org/10.1007/s00440-020-00988-5
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