Electronic Communications in Probability

On the Semi-classical Brownian Bridge Measure

Xue-Mei Li

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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.

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Electron. Commun. Probab. Volume 22 (2017), paper no. 38, 15 pp.

Received: 22 July 2016
Accepted: 20 June 2017
First available in Project Euclid: 4 August 2017

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Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60B05: Probability measures on topological spaces 60H07: Stochastic calculus of variations and the Malliavin calculus 58A12: de Rham theory [See also 14Fxx] 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 58B99: None of the above, but in this section

Malliavin calculus pinned path spaces loop spaces integration by parts Poincaré inequality

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Li, Xue-Mei. On the Semi-classical Brownian Bridge Measure. Electron. Commun. Probab. 22 (2017), paper no. 38, 15 pp. doi:10.1214/17-ECP69. https://projecteuclid.org/euclid.ecp/1501833630.

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