Compact Support Property of Super-Brownian Motion with Irregular Drift
- Authors: Leonid Mytnik, Johanna Weinberger
- Preprint year: 2026
- First public date: 2026-08-16
- arXiv: 2608.15616
Abstract
We study a one-dimensional stochastic partial differential equation describing super-Brownian motion with a bounded nonnegative drift that may be discontinuous at zero. Using a recursive layer decomposition into super-Brownian motions with immigration, we prove the compact support property, extend it by comparison to a broader class of drifts, and derive support-radius estimates that imply a positive extinction probability.