Lévy–Khintchine formula for Rough Paths

Stochastic Analysis Seminar Series


Abstract:  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.



ATUL SHEKHAR (Berlin University of Technology)

Monday, November 17, 2014 - 14:15
to 15:15