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Brownian motion and the distance to a submanifold
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Thompson, James (2016) Brownian motion and the distance to a submanifold. Potential Analysis, 45 (3). pp. 485-508. doi:10.1007/s11118-016-9553-2 ISSN 0926-2601.
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Official URL: http://dx.doi.org/10.1007/s11118-016-9553-2
Abstract
This is a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. It contains 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. The concentration inequality is derived 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.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Brownian movements, Submanifolds, Riemannian manifolds | ||||||||||
| Journal or Publication Title: | Potential Analysis | ||||||||||
| Publisher: | Springer Netherlands | ||||||||||
| ISSN: | 0926-2601 | ||||||||||
| Official Date: | October 2016 | ||||||||||
| Dates: |
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| Volume: | 45 | ||||||||||
| Number: | 3 | ||||||||||
| Page Range: | pp. 485-508 | ||||||||||
| DOI: | 10.1007/s11118-016-9553-2 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||
| Date of first compliant deposit: | 12 May 2016 | ||||||||||
| Date of first compliant Open Access: | 12 May 2016 | ||||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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