Title: Poincaré Inequality on the Path Space of Poisson Point Processes
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.