Functional inequalities on path space over a non-compact Riemannian manifold
Probability
2013-07-30 v2
Abstract
We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincar\'e inequality (and the super Poincar\'e inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on the path space over a general non-compact manifold.
Cite
@article{arxiv.1307.4482,
title = {Functional inequalities on path space over a non-compact Riemannian manifold},
author = {Xin Chen and Bo Wu},
journal= {arXiv preprint arXiv:1307.4482},
year = {2013}
}