Open Access
July 1999 Path Properties of Superprocesses with a General Branching Mechanism
Jean-François Delmas
Ann. Probab. 27(3): 1099-1134 (July 1999). DOI: 10.1214/aop/1022677441


We first consider a super Brownian motion $X$ with a general branching mechanism. Using the Brownian snake representation with subordination, we get the Hausdorff dimension of supp $X_t$, the topological support of $X_t$ and, more generally, the Hausdorff dimension of $\Bigcup_{t/in B}\supp X _t$. We also provide estimations on the hitting probability of small balls for those random measures. We then deduce that the support is totally disconnected in high dimension. Eventually, considering a super $\alpha$-stable process with a general branching mechanism, we prove that in low dimension this random measure is absolutely continuous with respect to the Lebesgue measure.


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Jean-François Delmas. "Path Properties of Superprocesses with a General Branching Mechanism." Ann. Probab. 27 (3) 1099 - 1134, July 1999.


Published: July 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0962.60033
MathSciNet: MR1733142
Digital Object Identifier: 10.1214/aop/1022677441

Primary: 60G57 , 60J25 , 60J55 , 60J80

Keywords: Brownian snake , exit mea-sure , Hausdorff dimension , hitting probabilities , measure valued processes , subordinator , Superprocesses

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 3 • July 1999
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