<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bogachev, L</style></author><author><style face="normal" font="default" size="100%">Daletskii, Alexei</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Poisson cluster measures: quasi-invariance, integration by parts and equilibrium stochastic dynamics</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Functional Analysis</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Stochastic Analysis</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://arxiv.org/abs/0803.4496</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">256</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">The distribution $\mu_{cl}$ of a Poisson cluster process in $X = R^d$ (with i.i.d. clusters) is studied
via an auxiliary Poisson measure on the space of configurations in disjoint union of the spaces $X^n$, with
intensity measure defined as a convolution of the background intensity of cluster centres
and the probability distribution of a generic cluster. We show that the measure $\mu_{cl}$ is quasiinvariant
with respect to the group of compactly supported diffeomorphisms of $X$ and prove
an integration-by-parts formula for $\mu_{cl}$. The corresponding equilibrium stochastic dynamics
is then constructed using the method of Dirichlet forms.</style></abstract><section><style face="normal" font="default" size="100%">432</style></section></record></records></xml>