LÉVY KHINTCHINE FORMULA FOR ROUGH PATHS

In this talk, we develop rough integration with jumps, offering a pathwise view on stochastic integration against cadlag processes.  A class of Marcus-like rough paths is introduced,which contains D. Williams’ construction of stochastic area for Lévy processes. We then established a Lévy–Khintchine type formula for the expected signature, based on“Marcus(canonical)"stochastic calculus. This calculus fails for non-Marcus-like Lévy rough paths and we treat the general case with Hunt’ theory of Lie group valued Lévy processes is made.