Besov rough path analysis

Abstract

Rough path analysis is developed in the full Besov scale. This extends, and essentially concludes, an investigation started by [Prömel--Trabs, Rough differential equations driven by signals in {B}esov spaces. J. Diff. Equ. 2016], further studied in a series of papers by Liu, Prömel 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 Hölder or variation settings. Important classes of stochastic processes fit in the present framework.

with an appendix by Pavel Zorin-Kranich