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July 2003 Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion
Leonid Mytnik, Edwin Perkins
Ann. Probab. 31(3): 1413-1440 (July 2003). DOI: 10.1214/aop/1055425785

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

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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

Information

Published: July 2003
First available in Project Euclid: 12 June 2003

zbMATH: 1042.60030
MathSciNet: MR1989438
Digital Object Identifier: 10.1214/aop/1055425785

Subjects:
Primary: 60G17, 60G57
Secondary: 60H15

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 3 • July 2003
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