Prof. Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology, NTNU)

In this talk, we consider a system of stochastic differential equations driven by Lévy processes and governed by non-commuting vector fields. We derive a series expansion of the logarithm of its flowmap, i.e., we compute a Chen-Strichartz formula. We provide an explicit formula for the components in this series; the vector fields are given in terms of the pre-Lie Magnus expansion generated by the original vector fields governing the stochastic differential equation. In particular, we show that the logarithm of the flowmap is a Lie series. These results extend previous work on the exponential Lie series for continuous semimartingales. This is joint work with Frederic Patras (CNRS, Nice), Anke Wiese (HWU, Edinburgh).