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Nontangential and probabilistic boundary behavior of pluriharmonic functions. (English) Zbl 1116.60040

For harmonic functions in the unit disc, the equivalence of the existence of a nontangential boundary limit and a limit along the Brownian path conditioned to go to that boundary point, was established by Doob. Even for dimension three, existence of a limit along the conditioned Brownian path, needs not to imply a nontangential boundary limit as shown by D. L. Burholder and R. F. Gundy [Ann. Inst. Fourier 23, No. 4, 195–212 (1973; Zbl 0253.31010)]. In this paper the author proves that these two modes of convergence are equivalent for pluri-harmonic functions in arbitrary dimensions.

MSC:

60J45 Probabilistic potential theory
60J65 Brownian motion
31B25 Boundary behavior of harmonic functions in higher dimensions

Citations:

Zbl 0253.31010
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References:

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