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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Detalles Bibliográficos
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
Descripción
Sumario: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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