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

Bogachev, L. and Daletskii, A. (2009) Poisson cluster measures:Quasi-invariance, integration by parts and equilibrium stochastic dynamics. Journal of Functional Analysis. pp. 432-478. ISSN 0022-1236

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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

Item Type: Article
Copyright, Publisher and Additional Information: © 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.
Keywords: Analysis
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Sherpa Assistant
Date Deposited: 15 Jan 2009 10:42
Last Modified: 22 Mar 2016 00:02
Published Version: http://dx.doi.org/10.1016/j.jfa.2008.10.009
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/5379

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