Mathematics – Functional Analysis
Scientific paper
2008-03-31
Mathematics
Functional Analysis
Revised version; has been accepted for publication in Journal of Functional Analysis
Scientific paper
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 $\mathfrak{X}=\sqcup_{n} X^n$, 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 quasi-invariant 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.
Bogachev Leonid
Daletskii Alexei
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