Communications in Mathematical Sciences
Volume 9 (2011)
Analysis on path spaces over Riemannian manifolds with boundary
Pages: 1203 – 1212
By using Hsu’s multiplicative functional for the Neumann heat equation, a natural damped gradient operator is defined for the reflecting Brownian motion on compact manifolds with boundary. This operator is linked to quasi-invariant flows in terms of an integration by parts formula, which leads to the standard log-Sobolev inequality for the associated Dirichlet form on the path space.
log-Sobolev inequality, integration by parts formula, path space over manifolds with boundary, reflecting Brownian motion
2010 Mathematics Subject Classification