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Brownian motion on an embedded manifold as the limit of Brownian motions with reflection in its tubular neighborhoods. (English. Russian original) Zbl 1053.60090
Math. Notes 73, No. 6, 895-899 (2003); translation from Mat. Zametki 73, No. 6, 947-950 (2003).
Introduction: A surface measure on the path space in a compact Riemannian manifold embedded in \(\mathbb{R}^n\) is studied. This measure is defined as the weak limit as \(\varepsilon\to 0\) of the family of measures \(\mathbb{W}_\varepsilon\) corresponding to the Brownian motion on \(\mathbb{R}^n\) starting at a point on the manifold with reflection on the boundary of the tubular \(\varepsilon\)-neighborhood of the manifold. We prove that this limit exists and the surface measure it defines coincides with the Wiener measure on the manifold.

MSC:
60J65 Brownian motion
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