Super-Brownian Motion with Irregular Drift

We establish weak existence and uniqueness for super-Brownian motion with certain irregular drift terms. The proof relies on an extension of the duality relation for super-Brownian motion, which allows us to treat a broad class of admissible drifts, including functions that are non-Lipschitz and even discontinuous at zero. In the proof, we use a log-Laplace equation  which is perturbed by jump noise as the equation for the dual process and the jumps of the dual process are allowed to take infinite values. We believe that the results for the dual process are also of independent interest.

The talk is based on joint work with Leonid Mytnik.