Characterization of Brownian motion on manifolds through integration by parts

Elton P. Hsu*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

9 Scopus citations


Inspired by Stein’s theory in mathematical statistics, we show that the Wiener measure on the pinned path space over a compact Riemannian manifold is uniquely characterized by its integration by parts formula among the set of probability measures on the path space for which the coordinate process is a semimartingale. Because of the presence of the curvature, the usual proof will not be readily extended to this infinite dimensional setting. Instead, we show that the integration by parts formula implies that the stochastic anti-development of the coordinate process satisfies Lévy’s criterion.

Original languageEnglish (US)
Title of host publicationStein’s Method and Applications
PublisherWorld Scientific Publishing Co.
Number of pages14
ISBN (Electronic)9789812567673
ISBN (Print)9812562818
StatePublished - Jan 1 2005

ASJC Scopus subject areas

  • Mathematics(all)


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