%0 Journal Article
%T Poincare Inequality on the Path Space of Poisson Point Processes
%A Feng-Yu Wang
%A Chenggui Yuan
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0801.2668v2