[en] 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.
Disciplines :
Mathématiques
Auteur, co-auteur :
THOMPSON, James ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Brownian bridges to submanifolds
Date de publication/diffusion :
2018
Titre du périodique :
Potential Analysis
ISSN :
0926-2601
eISSN :
1572-929X
Maison d'édition :
Springer, Amsterdam, Pays-Bas
Peer reviewed :
Peer reviewed vérifié par ORBi
Projet FnR :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
