Superdiffusive limits for deterministic fast-slow dynamical systems

Ilya Chevyrev, Alexey Korepanov, Peter K. Friz, Ian Melbourne

Research output: Contribution to journalArticlepeer-review

Abstract

We consider deterministic fast-slow dynamical systems onRm×Yof the form{x(n)k+1=x(n)k+n−1a(x(n)k) +n−1/αb(x(n)k)v(yk),yk+1=f(yk),whereα∈(1,2). Under certain assumptions we prove convergence of them-dimensional processXn(t) =x(n)⌊nt⌋to the solution of the stochastic differential equationdX=a(X) dt+b(X)⋄dLα,whereLαis anα-stable Lvy process and⋄indicates that the stochastic integral is in theMarcus sense. In addition, we show that our assumptions are satisfied for intermittentmapsfof Pomeau-Manneville type.
Original languageEnglish
Pages (from-to)735–770
Number of pages36
JournalProbability theory and related fields
Volume178
Early online date16 Jul 2020
DOIs
Publication statusPublished - 31 Dec 2020

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