A distributional approach to multiple stochastic integrals and transformations of the Poisson measure. II
type: Item
instance of: scholarly article
title: A distributional approach to multiple stochastic integrals and transformations of the Poisson measure. II
zbMATH Open document ID: 1153.28010
author: N. V. Smorodina
author: S. Albeverio
published in: Acta Applicandae Mathematicae
publication date: 2008-07-30T00:00:00Z
review text: The authors develop an analysis on the space of configurations over the space \(G=S\times{\mathbb R}\), where \(S\) is a complete separable metric space. On this configuration space they consider the Poisson measure \(P\) with intensity measure \(\pi\times\gamma\), where \(\pi\) is a finite measure on \(S\) and \(\gamma\) is a \(\sigma\)-finite measure on \(\mathbb R\) with a singularity at the origin. Let \({\mathcal X}={\mathcal X}(G)\) be the space of locally finite configurations on a metric space \(G\). Let \(F\) be a measurable mapping \(F:{\mathcal X}\to{\mathcal X}\), and \(PF^{-1}\) be the corresponding transformation of the measure \(P\). This transformation is ``nonpoissonian''. This means that the ``new'' position of each point depends not only on the ``old'' position but also on other points of the configuration. The authors find conditions such that the measure \(PF^{-1}\) is absolutely continuous with respect to the measure \(P\) and get then the expression for the corresponding Radon-Nikodym derivative \(\frac{dPF^{-1}}{dP}\). For part I, cf. Acta Appl. Math. 94, No. 1, 1--19 (2006; Zbl 1107.28010).
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 5306232
zbMATH Keywords: Poisson random measures
zbMATH Keywords: multiple stochastic integrals
zbMATH Keywords: absolute continuity
zbMATH Keywords: Radon-Nikodym derivative
MaRDI profile type: Publication
full work available at URL: s10440-008-9223-5
OpenAlex ID: W2006490697
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DOI: 10.1007/S10440-008-9223-5
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description: scientific article; zbMATH DE number 5306232