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.

 

Location:
Speaker(s):

ATUL SHEKHAR (Berlin University of Technology)

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