Nontangential and probabilistic boundary behavior of pluriharmonic functions

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dc.creatorTanner, Steve
dc.date2005-11-15
dc.date2006-09-25
dc.date.accessioned2026-07-07T06:51:15Z
dc.date.available2026-07-07T06:51:15Z
dc.descriptionLet $u$ be a pluriharmonic function on the unit ball in $\mathbb{C}^n$. I consider the relationship between the set of points $L_u$ on the boundary of the ball at which $u$ converges nontangentially and the set of points $\mathcal{L}_u$ at which $u$ converges along conditioned Brownian paths. For harmonic functions $u$ of two variables, the result $L_u\stackrel{\mathrm{a.e.}}{=}\mathcal{L}_u$ has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the $L_u\stackrel{\mathrm{a.e.}}{=}\mathcal{L}_u$ result to pluriharmonic functions in arbitrary dimensions.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117906000000188 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0511368
dc.identifierhttp://arxiv.org/abs/math/0511368
dc.identifierAnnals of Probability 2006, Vol. 34, No. 4, 1623-1634
dc.identifierdoi:10.1214/009117906000000188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104924
dc.subjectProbability
dc.subjectComplex Variables
dc.subject60J45, 32A40 (Primary) 60J65 (Secondary)
dc.titleNontangential and probabilistic boundary behavior of pluriharmonic functions
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