2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173112The 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.Probability60H10;47G20text