Poincare Inequality on the Path Space of Poisson Point Processes

Details Poincare Inequality on the Path Space of Poisson Point Processes Poincare Inequality on the Path Space of Poisson Point Processes

2008-01-17

arxiv.org/abs/0801.2668v2

Mathematics

Probability

Scientific paper

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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