We prove an integration by parts formula for the probability measure on the pinned path space induced by the Semi-classical Riemmanian Brownian Bridge, over a manifold with a pole, followed by a discussion on its equivalence with the Brownian Bridge measure.
"On the Semi-classical Brownian Bridge Measure." Electron. Commun. Probab. 22 1 - 15, 2017. https://doi.org/10.1214/17-ECP69