Brownian bridges to submanifolds
Probability
2017-03-21 v2
Abstract
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold.
Cite
@article{arxiv.1604.05182,
title = {Brownian bridges to submanifolds},
author = {James Thompson},
journal= {arXiv preprint arXiv:1604.05182},
year = {2017}
}