## The Annals of Probability

### Path Properties of Superprocesses with a General Branching Mechanism

Jean-François Delmas

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 27, Number 3 (1999), 1099-1134.

Dates
First available in Project Euclid: 29 May 2002

https://projecteuclid.org/euclid.aop/1022677441

Digital Object Identifier
doi:10.1214/aop/1022677441

Mathematical Reviews number (MathSciNet)
MR1733142

Zentralblatt MATH identifier
0962.60033

#### Citation

Delmas, Jean-François. Path Properties of Superprocesses with a General Branching Mechanism. Ann. Probab. 27 (1999), no. 3, 1099--1134. doi:10.1214/aop/1022677441. https://projecteuclid.org/euclid.aop/1022677441

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