Poisson Cluster Measures: Quasi-invariance, Integration by Parts and Equilibrium Stochastic Dynamics

Leonid Bogachev, Alexei Daletskii

The distribution ${\mu }_{cl}$ of a Poisson cluster process in $X={\mathbb{R}}^d$ (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in $\…