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A priori bounds for rough differential equations with a non-linear damping term
File | Description | Size | Format | |
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boundsrde.pdf | Accepted version | 637.26 kB | Adobe PDF | View/Open |
Title: | A priori bounds for rough differential equations with a non-linear damping term |
Authors: | Bonnefoi, T Chandra, A Moinat, A Weber, H |
Item Type: | Journal Article |
Abstract: | We consider a rough differential equation with a non-linear damping drift term: dY (t) = −|Y |m−1Y (t)dt + σ (Y (t))dX(t), where m>1, X is a (branched) rough path of arbitrary regularity α>0, and where σ is smooth and satisfies an m and α-dependent growth property. We show a strong a priori bound for Y, which includes the “coming down from infinity” property, i.e. the bound on Y(t) for a fixed t>0 holds uniformly over all choices of initial datum Y(0). The method of proof builds on recent work on a priori bounds for the ϕ4 SPDE in arbitrary subcritical dimension [7]. A key new ingredient is an extension of the algebraic framework which permits to derive an estimate on higher order conditions of a coherent controlled rough path in terms of the regularity condition at lowest level. |
Issue Date: | 5-May-2022 |
Date of Acceptance: | 4-Feb-2022 |
URI: | http://hdl.handle.net/10044/1/96114 |
DOI: | 10.1016/j.jde.2022.02.006 |
ISSN: | 0022-0396 |
Publisher: | Elsevier BV |
Start Page: | 58 |
End Page: | 93 |
Journal / Book Title: | Journal of Differential Equations |
Volume: | 318 |
Copyright Statement: | © 2022 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Keywords: | 0101 Pure Mathematics 0102 Applied Mathematics General Mathematics |
Publication Status: | Published online |
Online Publication Date: | 2022-02-24 |
Appears in Collections: | Pure Mathematics Mathematics |
This item is licensed under a Creative Commons License