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This article presents a purely functional-analytic construction of theconcept of stochastic parallel transport in Hermitian bundles over Riemannianmanifolds. As a byproduct, we also obtain a form of the Feynman-Kac formula invector bundles that is, to our best knowledge, the most general found so far.

A functional-analytic construction of the stochastic parallel transport in Hermitian bundles over Riemannian manifolds