We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.
"Multifractal analysis of superprocesses with stable branching in dimension one." Ann. Probab. 43 (5) 2763 - 2809, September 2015. https://doi.org/10.1214/14-AOP951