Brownian motion conditioned to a thin tubular neighbourhood of a submanifold of a Riemannian manifold converges in finite-dimensional distributions to Brownian motion on the submanifold.
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A Convergence Result for Dirichlet Semigroups on Tubular Neighbourhoods and the Marginals of Conditional Brownian Motion
Brownian motion conditioned to a thin tubular neighbourhood of a submanifold of a Riemannian manifold converges in finite-dimensional distributions to Brownian motion on the submanifold.