Poincaré Inequality on the Path Space of Poisson Point Processes

Feng-Yu Wang () and Chenggui Yuan ()
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Feng-Yu Wang: Beijing Normal University
Chenggui Yuan: Swansea University

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 824-833

Abstract: Abstract Quasi-invariance is proved for the distributions of Poisson point processes under a random shift map on the path space. This leads to a natural Dirichlet form of jump type on the path space. Differently from the O–U Dirichlet form on the Wiener space satisfying the log-Sobolev inequality, this Dirichlet form merely satisfies the Poincaré inequality but not the log-Sobolev one.

Keywords: Poincaré inequality; Path space; Quasi-invariance; Dirichlet form; Poisson processes; 60H10; 47G20 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0232-8

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