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Functional limit theorems for volterra processes and applications to homogenization

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Title: Functional limit theorems for volterra processes and applications to homogenization
Authors: Gehringer, J
Li, X-M
Sieber, J
Item Type: Journal Article
Abstract: We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process (yt)t≥0 in the rough path topology. As an application, we establish weak convergence as ε→0 of the solution of the random ordinary differential equation (ODE) ddtxεt=1ε√f(xεt,ytε) and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the Lévy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of the random ODE converge to those of the Kunita type Itô SDE dxt=G(xt,dt), where G(x,t) is a semi-martingale with spatial parameters.
Issue Date: 1-Mar-2022
Date of Acceptance: 5-Jan-2022
URI: http://hdl.handle.net/10044/1/94071
DOI: 10.1088/1361-6544/ac4818
ISSN: 0951-7715
Publisher: IOP Publishing
Start Page: 1
End Page: 37
Journal / Book Title: Nonlinearity
Volume: 35
Issue: 4
Copyright Statement: © 2022 IOP Publishing Ltd & London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Sponsor/Funder: EPSRC
Engineering and Physical Sciences Research Council
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/S023925/1
Keywords: 0102 Applied Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2022-03-01
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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