The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold

N.A. Sidorova, O.G. Smolyanov, H. Weizsäcker, von, O. Wittich

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    17 Citations (Scopus)

    Abstract

    We construct the surface measure on the space C([0,1],M) of paths in a compact Riemannian manifold M without boundary embedded into which is induced by the usual flat Wiener measure on conditioned to the event that the Brownian particle does not leave the tubular -neighborhood of M up to time 1. We prove that the limit as ¿0 exists, the limit measure is equivalent to the Wiener measure on C([0,1],M), and we compute the corresponding density explicitly in terms of scalar and mean curvature.
    Original languageEnglish
    Pages (from-to)391-413
    JournalJournal of Functional Analysis
    Volume206
    Issue number2
    DOIs
    Publication statusPublished - 2004

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