Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics

TY - JOUR

T1 - Poisson cluster measures

T2 - Quasi-invariance, integration by parts and equilibrium stochastic dynamics

AU - Bogachev, L.

AU - Daletskii, A.

N1 - © 2009 Elsevier B.V. This is an author produced version of a paper published in Journal of Functional Analysis. Uploaded in accordance with the publisher's self archiving policy.

PY - 2009/1/15

Y1 - 2009/1/15

N2 - The distribution µcl of a Poisson cluster process in X = Rd (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in X = FnXn, 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 µcl is quasiinvariant with respect to the group of compactly supported diffeomorphisms ofX and prove an integration-by-parts formula for µcl. The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms

AB - The distribution µcl of a Poisson cluster process in X = Rd (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in X = FnXn, 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 µcl is quasiinvariant with respect to the group of compactly supported diffeomorphisms ofX and prove an integration-by-parts formula for µcl. The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms

UR - http://www.scopus.com/inward/record.url?scp=56549122302&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2008.10.009

DO - 10.1016/j.jfa.2008.10.009

M3 - Article

SN - 0022-1236

VL - 256

SP - 432

EP - 478

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -