Rough differential equations on Besov spaces

David J. Prömel, Mathias Trabs

Published 2015-06-10Version 1

Rough differential equations are solved for signals in general Besov spaces unifying in particular the known results in H\"older and p-variation topology. To this end the paracontrolled distribution approach, which has been introduced by Gubinelli, Imkeller and Perkowski ["Paracontrolled distribution and singular PDEs" to appear in Forum of Mathematics, Pi] to analyze singular stochastic PDEs, is extended from H\"older to Besov spaces. As an application we solve stochastic differential equations driven by random functions in Besov spaces and Gaussian processes in a pathwise sense.