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July 2022 Lipschitz-stability of Controlled Rough Paths and Rough Differential Equations
Horatio Boedihardjo, Xi Geng
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Osaka J. Math. 59(3): 653-682 (July 2022).

Abstract

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 $\alpha$-Hölder continuous for $\alpha>1/3$ is widely available in the literature. In its extension to the case when $\alpha\leqslant1/3,$ 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.

Acknowledgments

The author XG is supported by the ARC grant DE210101352.

Citation

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Horatio Boedihardjo. Xi Geng. "Lipschitz-stability of Controlled Rough Paths and Rough Differential Equations." Osaka J. Math. 59 (3) 653 - 682, July 2022.

Information

Received: 16 November 2020; Revised: 31 May 2021; Published: July 2022
First available in Project Euclid: 23 June 2022

Subjects:
Primary: 34A12 , 34H99
Secondary: 17B01 , 60H10

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 3 • July 2022
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