Besov rough path analysis

TL;DR

This paper extends rough path analysis to the full Besov space scale, introducing a new Besov sewing lemma, enabling the study of equations and stochastic processes not manageable with traditional methods.

Contribution

It develops a comprehensive Besov rough path framework, including a novel sewing lemma, broadening the scope of rough path analysis beyond H"older and variation settings.

Findings

Introduces a new Besov sewing lemma.

Extends rough path analysis to Besov spaces.

Enables treatment of new classes of stochastic processes.

Abstract

Rough path analysis is developed in the full Besov scale. This extends, and essentially concludes, an investigation started by [Pr\"omel--Trabs, Rough differential equations driven by signals in {B}esov spaces. J. Diff. Equ. 2016], further studied in a series of papers by Liu, Pr\"omel and Teichmann. A new Besov sewing lemma, a real-analysis result of interest in its own right, plays a key role, and the flexibility in the choice of Besov parameters allows for the treatment of equations not available in the H\"older or variation settings. Important classes of stochastic processes fit in the present framework.