基于正则结构的Sobolev粗糙路径扩展定理

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

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引用次数: 3

摘要

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。

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A Sobolev rough path extension theorem via regularity structures

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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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

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.