Feng-Yu Wang, Chenggui Yuan
Published 2008-01-17, updated 2008-11-05Version 2
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.
A Note on the Paper $"$Poincaré Inequality on the Path Space of Poisson Point Processes"
Functional inequalities on path space over a non-compact Riemannian manifold
Poisson point processes: Large deviation inequalities for the convex distance
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