Batu Güneysu
Published 2016-04-28Version 1
I prove that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with connection, including its terminal time. The proof is based on a localized Hamilton-type gradient estimate by Arnaudon/Thalmaier.
Two recursive decompositions of Brownian bridge
One more approach to the convergence of the empirical process to the Brownian bridge
On the loss of the semimartingale property at the hitting time of a level
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