Electronic Communications in Probability

On the Semi-classical Brownian Bridge Measure

Xue-Mei Li

Full-text: Open access

Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1501833630

Digital Object Identifier
doi:10.1214/17-ECP69

Subjects
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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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