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July 1998 Kolmogorov's test for super-Brownian motion
Jean-Stéphane Dhersin, Jean-François Le Gall
Ann. Probab. 26(3): 1041-1056 (July 1998). DOI: 10.1214/aop/1022855744


We prove a Kolmogorov test for super-Brownian motion started at the Dirac mass at the origin. More precisely, we determine the functions $g$ such that for all $t$ small enough, the support of the process at time $t$ will be contained in the ball of radius $g(t)$ centered at 0. As a consequence, we get a necessary and sufficient condition for the existence in certain space-time domains of a solution of the associated semilinear partial differential equation that blows up at the origin.


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Jean-Stéphane Dhersin. Jean-François Le Gall. "Kolmogorov's test for super-Brownian motion." Ann. Probab. 26 (3) 1041 - 1056, July 1998.


Published: July 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60087
MathSciNet: MR1634414
Digital Object Identifier: 10.1214/aop/1022855744

Primary: 60G17 , 60J80
Secondary: 60G57

Keywords: Brownian snake , Exit measure , Kolmogorov test , semilinear partial differential equation , Super-Brownian motion

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 3 • July 1998
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