## The Annals of Probability

### Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion

#### 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.

#### Article information

Source
Ann. Probab. Volume 31, Number 3 (2003), 1413-1440.

Dates
First available in Project Euclid: 12 June 2003

http://projecteuclid.org/euclid.aop/1055425785

Digital Object Identifier
doi:10.1214/aop/1055425785

Mathematical Reviews number (MathSciNet)
MR1989438

Zentralblatt MATH identifier
02072325

#### Citation

Mytnik, Leonid; Perkins, Edwin. Regularity and irregularity of $\bolds{(1+\beta)}$-stable super-Brownian motion. Ann. Probab. 31 (2003), no. 3, 1413--1440. doi:10.1214/aop/1055425785. http://projecteuclid.org/euclid.aop/1055425785.

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• VANCOUVER, BRITISH COLUMBIA CANADA V6T 1Z2 E-MAIL: perkins@math.ubc.ca