Poisson Cluster Measures: Quasi-invariance, Integration by Parts and Equilibrium Stochastic Dynamics
| dc.creator | Bogachev, Leonid | |
| dc.creator | Daletskii, Alexei | |
| dc.date | 2008-03-31 | |
| dc.date | 2008-10-07 | |
| dc.date.accessioned | 2026-07-07T10:07:36Z | |
| dc.date.available | 2026-07-07T10:07:36Z | |
| dc.description | The distribution $μ_{cl}$ 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 $μ_{cl}$ is quasi-invariant with respect to the group of compactly supported diffeomorphisms of $X$ and prove an integration-by-parts formula for $μ_{cl}$. The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. | |
| dc.description | Revised version; has been accepted for publication in Journal of Functional Analysis | |
| dc.identifier | https://arxiv.org/abs/0803.4496 | |
| dc.identifier | http://arxiv.org/abs/0803.4496 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170692 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 58J65 (Primary); 31C25, 46G12, 60G55, 70F45 (Secondary) | |
| dc.title | Poisson Cluster Measures: Quasi-invariance, Integration by Parts and Equilibrium Stochastic Dynamics | |
| dc.type | text |