Path Properties of Superprocesses with a General Branching Mechanism

Delmas, Jean-François

Ann. Probab., Tome 27 (1999) no. 1, p. 1099-1134 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1999-07-14
Classification:  Superprocesses,  measure valued processes,  Brownian snake,  exit mea-sure,  hitting probabilities,  Hausdorff dimension,  subordinator,  60G57,  60J25,  60J55,  60J80