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January 2005 Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion
Jean-François Le Gall, Leonid Mytnik
Ann. Probab. 33(1): 194-222 (January 2005). DOI: 10.1214/009117904000000612

Abstract

This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1+β)-stable branching mechanism. It establishes the continuity of the density in dimension d=2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutions of the partial differential equation Δu=u1+β.

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Jean-François Le Gall. Leonid Mytnik. "Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion." Ann. Probab. 33 (1) 194 - 222, January 2005. https://doi.org/10.1214/009117904000000612

Information

Published: January 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1097.60033
MathSciNet: MR2118864
Digital Object Identifier: 10.1214/009117904000000612

Subjects:
Primary: 60G57
Secondary: 35J65 , 60G17 , 60J80

Keywords: Exit measure , martingale measure , semilinear partial differential equation , stochastic integral representation , Super-Brownian motion

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • January 2005
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