Reference : Brownian motion and the distance to a submanifold
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/26517
Brownian motion and the distance to a submanifold
English
Thompson, James mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2016
Potential Analysis
Springer
Yes (verified by ORBilu)
0926-2601
1572-929X
Amsterdam
The Netherlands
[en] Brownian motion ; submanifold ; local time ; tube ; distance
[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.
EPSRC
http://hdl.handle.net/10993/26517
10.1007/s11118-016-9553-2
The original publication is available at www.springerlink.com

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