On the semimartingale property of Brownian bridges on complete manifolds
  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. 
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math.PR math.AP math.DG