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On the semi-classical Brownian bridge measure. (English) Zbl 1378.60031
Summary: 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.

MSC:
60D05 Geometric probability and stochastic geometry
60B05 Probability measures on topological spaces
60H07 Stochastic calculus of variations and the Malliavin calculus
58J65 Diffusion processes and stochastic analysis on manifolds
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