Brossard, Jean; Chevalier, Lucien 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 J. Reine Angew. Math. 421, 141-157 (1991). 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 Keywords:Brownian convergence in probability; semi-fine convergence; potential theoretic characterization of non-tangential convergence PDFBibTeX XMLCite \textit{J. Brossard} and \textit{L. Chevalier}, J. Reine Angew. Math. 421, 141--157 (1991; Zbl 0731.60031) Full Text: EuDML