  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.
