Poincare Inequality on the Path Space of Poisson Point Processes
Probability
2008-11-05 v2
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.
Keywords
Cite
@article{arxiv.0801.2668,
title = {Poincare Inequality on the Path Space of Poisson Point Processes},
author = {Feng-Yu Wang and Chenggui Yuan},
journal= {arXiv preprint arXiv:0801.2668},
year = {2008}
}