A stochastic approach to quasi-everywhere boundary convergence of harmonic functions

DOI10.1016/0022-1236(87)90077-2zbMath0636.60078OpenAlexW2063422697MaRDI QIDQ1098176

Rodrigo Bañuelos, Bernt Øksendal

Publication date: 1987

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90077-2

zbMATH Keywords

capacitysymmetric Markov processstrong Markov processregularity assumptionsboundary convergence of harmonic functionsDoob's h-transform

Mathematics Subject Classification ID

Brownian motion (60J65) Probabilistic potential theory (60J45) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items

Harmonic extension technique for non-symmetric operators with completely monotone kernels ⋮ Boundary traces of shift-invariant diffusions in half-plane ⋮ Traces of harmonic functions, capacities, and traces of symmetric Markov processes

Cites Work

• Stochastic differential equations. An introduction with applications
• Brownian motion and analytic functions
• Boundary behavior of harmonic functions in a half-space and Brownian motion
• Conditional brownian motion and the boundary limits of harmonic functions
• A Maximal Function Characterization of the Class H p
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