  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.
