Rough Stochastic Analysis with Jumps

Abstract: We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c`adl`ag setting. In particular, we define rough stochastic integration and establish solutions to rough stochastic differential equations with jump discontinuities in both sources of noise, along with an It^o formula for stochastic controlled paths with jumps.