Local approximation and conditioning in Dawson-Watanabe superprocesses

Jeudi 15 mai 2008 14:00-15:00 - Kallenberg Olav - Auburn University

Résumé : We consider a critical, measure-valued branching diffusion $\xi$ in $R^d$, where the branching is continuous and the spatial motion is given by the heat flow. For $d \geq 2$ and $t > 0$, it is known to be an a.s. singular random measure of Hausdorff dimension 2. We explain how it can be approximated by Lebesgue measure on $\varepsilon$-neighborhoods of the support. Next we show how
$\xi_t$ can be approximated in total variation near $n$ points, and how the associated Palm distributions arise in the limit from elementary conditioning. Finally, we hope to explain the duality between moment and Palm measures and to show how the latter can be described in terms of discrete « Palm trees. »

Lieu : bât. 425 - 117-119

Local approximation and conditioning in Dawson-Watanabe superprocesses  Version PDF