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Poincaré Inequality on the Path Space of Poisson Point Processes

Author

Listed:
  • Feng-Yu Wang

    (Beijing Normal University
    Swansea University)

  • Chenggui Yuan

    (Swansea University)

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.

Suggested Citation

  • Feng-Yu Wang & Chenggui Yuan, 2010. "Poincaré Inequality on the Path Space of Poisson Point Processes," Journal of Theoretical Probability, Springer, vol. 23(3), pages 824-833, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-009-0232-8
    DOI: 10.1007/s10959-009-0232-8
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