On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold

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.