A priori bounds for rough differential equations with a non-linear damping term
File(s)
Accepted version
Author(s)
Bonnefoi, Timothée
Chandra, Ajay
Moinat, Augustin
Weber, Hendrik
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.
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.
Date Issued
2022-05-05
Date Acceptance
2022-02-04
Citation
Journal of Differential Equations, 2022, 318, pp.58-93
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/
Identifier
https://www.sciencedirect.com/science/article/pii/S0022039622000924?via%3Dihub
Subjects
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status
Published online
Date Publish Online
2022-02-24