Article (Scientific journals)
Brownian motion and the distance to a submanifold
Thompson, James
2016In Potential Analysis
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Keywords :
Brownian motion; submanifold; local time; tube; distance
Abstract :
[en] We present a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. We include a variety of results, including an inequality for the Laplacian of the distance function derived from a Jacobian comparison theorem, a characterization of local time on a hypersurface which includes a formula for the mean local time, an exit time estimate for tubular neighbourhoods and a concentration inequality. We derive the concentration inequality using moment estimates to obtain an exponential bound, which holds under fairly general assumptions and which is sufficiently sharp to imply a comparison theorem. We provide numerous examples throughout. Further applications will feature in a subsequent article, where we see how the main results and methods presented here can be applied to certain study objects which appear naturally in the theory of submanifold bridge processes.
Disciplines :
Mathematics
Author, co-author :
Thompson, James ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Brownian motion and the distance to a submanifold
Publication date :
2016
Journal title :
Potential Analysis
ISSN :
1572-929X
Publisher :
Springer, Amsterdam, Netherlands
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
EPSRC - Engineering and Physical Sciences Research Council [GB]
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since 08 April 2016

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