Cadlag curves of SLE driven by Levy processes

Abstract

Schramm Loewner Evolutions (SLE) are random increasing hulls defined through the Loewner equation driven by Brownian motion. It is known that the increasing hulls are generated by continuous curves. When the driving process is of the form \sqrt{\kappa} B+\theta^{1/\alpha}S for a Brownian motion B and a symmetric \alpha-stable process S with \kappa not equal to 4 and 8, we prove that the corresponding increasing hulls are generated by Cadlag curves.