Boundary behavior and optimal pointwise Hölder exponent of the total local time of $(1+\beta )$-stable super-Brownian motion

Jieliang Hong, Du Yang, Junyan Zhang

Let $L^x$ be the total local time of one-dimensional super-Brownian motion with $(1+\beta )$-stable branching mechanism, $0<\beta <1$. We prove that $\{x\in \mathbb{R}:L^x>0\}$ is almost surel…