LIPSCHITZ-STABILITY OF CONTROLLED ROUGH PATHS AND ROUGH DIFFERENTIAL EQUATIONS

被引：0

作者：

Boedihardjo, Horatio ^{[1
]}

Geng, Xi ^{[2
]}

机构：

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

来源：

OSAKA JOURNAL OF MATHEMATICS | 2022年 / 59卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

DRIVEN;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide an account for the existence and uniqueness of solutions to rough differential equations in infinite dimensions under the framework of controlled rough paths. The case when the driving path is alpha-Holder continuous for alpha > 1/3 is widely available in the literature. In its extension to the case when a <= 1/3, the main challenge and missing ingredient is to show that controlled rough paths are closed under composition with Lipschitz transformations. Establishing such a property precisely, which has a strong algebraic nature, is a main purpose of the present article.

引用

页码：653 / 682

页数：30

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