Lipschitz estimates in the Besov settings for Young and rough differential equations

TL;DR

This paper introduces new techniques to translate rough path analysis into Besov space analysis, providing precise Lipschitz estimates for Young and rough differential equations in both variation and Besov scales.

Contribution

It develops novel metric groups that reinterpret rough path objects as path increments, enabling effective Besov rough analysis and precise Lipschitz estimates.

Findings

Effective recovery of Besov rough analysis from p-variation analysis

Introduction of new metric groups for rough path objects

Precise Lipschitz estimates for Young and rough differential equations

Abstract

We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as two-parameter can be considered as path increments. Furthermore, we develop highly precise Lipschitz estimates for Young and rough differential equations, both in the variation and Besov scale.