Abstract
In this paper, we focus on the characterization of a Brownian bridge measure on the pinned path space over a compact Riemannian manifold. In the case when the Riemannian manifold is simply connected, we prove that the integration by parts formula can characterize the Brownian bridge measure. Otherwise, we show that it is not always true by constructing an illustrating example.
Funding Statement
The first author was supported by the National Natural Science Foundation of China under grants 11688101. The second author was supported by the National Natural Science Foundation of China under grants 11801064.
Acknowledgments
The authors are very grateful for the comments and suggestions from the editor and the anonymous referees which helped to improve the presentation.
Citation
Fuzhou Gong. Xiaoxia Sun. "On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold." Bernoulli 28 (4) 2322 - 2344, November 2022. https://doi.org/10.3150/21-BEJ1420
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