Analysis on Path Spaces over Riemmannian Manifolds with Boundary

Details Analysis on Path Spaces over Riemmannian Manifolds with Boundary Analysis on Path Spaces over Riemmannian Manifolds with Boundary

2010-02-15

arxiv.org/abs/1002.2887v1

Mathematics

Probability

14 pages

Scientific paper

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 a integration by parts formula, which leads to the standard
log-Sobolev inequality for the associated Dirichlet form on the path space.

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