Abstract
This paper establishes the continuity of the density of $(1+\beta)$-stable super-Brownian motion $(0<\beta<1)$ for fixed times in $d=1$, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions $d\geq2$ where the local time exists.
Citation
Leonid Mytnik. Edwin Perkins. "Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion." Ann. Probab. 31 (3) 1413 - 1440, July 2003. https://doi.org/10.1214/aop/1055425785
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