The York Research Database

The distribution mu of a Poisson cluster process in chi = R-d (with n-point clusters) is studied via the projection of an auxiliary Poisson measure in the space of configurations in chi(n), with the intensity measure being the convolution of the background intensity (of cluster centres) with the probability distribution of a generic cluster. We show that mu is quasi-invariant with respect to the group of compactly supported diffeomorphisms of chi, and prove an integration by parts formula for mu. The corresponding equilibrium. stochastic dynamics is then constructed using the method of Dirichlet forms.