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Limites non tangentielles, limites browniennes en probabilité et limites semi-fines. (Non-tangential limits, Brownian limits in probability and semi-fine limits). (French) Zbl 0731.60031

Summary: We introduce a notion of Brownian convergence in probability, allowing us to obtain a probabilistic characterization of non-tangential convergence at an individual boundary point, for an arbitrary harmonic function defined on the half-space. Moreover, it turns out that Brownian convergence in probability is closely related to semi-fine convergence, thus providing a potential theoretic characterization of non-tangential convergence.

MSC:

60F99 Limit theorems in probability theory
60J45 Probabilistic potential theory
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