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arXiv · 0801.2668

Poincare Inequality on the Path Space of Poisson Point Processes

Feng-Yu Wang·Chenggui Yuan
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Abstract

The 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 Poincare inequality but not the log-Sobolev one.

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Feng-Yu Wang, Chenggui Yuan. 2008-11-05. Poincare Inequality on the Path Space of Poisson Point Processes. https://arxiv.org/abs/0801.2668

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