A Sobolev rough path extension theorem via regularity structures

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2021-04-13 DOI:10.1051/ps/2022016

Chong Liu, David J. Promel, J. Teichmann

引用次数: 3

Abstract

We show that every $\R^d$-valued Sobolev path with regularity~$\alpha$ and integrability~$p$ can be lifted to a Sobolev rough path provided $1/2 >\alpha > 1/p \vee 1/3$. The novelty of our approach is its use of ideas underlying Hairer's reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.

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基于正则结构的Sobolev粗糙路径扩展定理

我们证明了只要$1/2 >\ α > 1/p \v / 1/3$，具有正则性~$\ α $和可积性~$p$的每$\R^d$值的Sobolev路径都可以提升为Sobolev粗路径。我们的方法的新颖之处在于它使用了基于harer重建定理的思想，将其推广到一个允许Sobolev模型和Sobolev建模分布的框架。此外，我们还证明了相应的提升映射相对于非齐次Sobolev度规是局部Lipschitz连续的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

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