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A priori bounds for rough differential equations with a non-linear damping term | | Timothee Bonnefoi
; Ajay Chandra
; Augustin Moinat
; Hendrik Weber
; | | Date: |
12 Nov 2020 | | Abstract: | We consider a rough differential equation with a non-linear damping drift
term: egin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + sigma(Y(t)) dX(t),
end{align*} where $X$ is a branched rough path of arbitrary regularity $alpha
>0$, $m>1$ and where $sigma$ is smooth and satisfies an $m$ and
$alpha$-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 by Chandra, Moinat and Weber on a
priori bounds for the $phi^4$ SPDE in arbitrary subcritical dimension. 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. | | Source: | arXiv, 2011.06645 | | Services: | Forum | Review | PDF | Favorites | |
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