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- W2950646706 abstract "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." @default.
- W2950646706 created "2019-06-27" @default.
- W2950646706 creator A5002354353 @default.
- W2950646706 date "2015-05-27" @default.
- W2950646706 modified "2023-09-27" @default.
- W2950646706 title "Brownian motion and the distance to a submanifold" @default.
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