A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

Greg Markowsky

doi:10.1016/j.jmaa.2018.04.045

A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

Greg Markowsky

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

A new proof is given of a simple probabilistic lemma which implies the solution of the Dirichlet problem for simply connected domains in the plane. This proof uses the conformal invariance of planar Brownian motion in place of the previously existing measure-theoretic arguments.

Original language	English
Pages (from-to)	1143-1146
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	464
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.04.045
Publication status	Published - 15 Aug 2018

Keywords

Analytic functions
Dirichlet problem
Planar Brownian motion

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10.1016/j.jmaa.2018.04.045

Cite this

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abstract = "A new proof is given of a simple probabilistic lemma which implies the solution of the Dirichlet problem for simply connected domains in the plane. This proof uses the conformal invariance of planar Brownian motion in place of the previously existing measure-theoretic arguments.",

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KW - Planar Brownian motion

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A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

Abstract

Keywords

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Other files and links

Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this

A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

Abstract

Keywords

Access to Document

Other files and links

Projects

Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this