An Intuitive Approach to the Martin Boundary
Peter A. Loeb
TL;DR
This paper introduces an intuitive probabilistic method for constructing the Martin boundary and maximal representing measures for positive harmonic functions, offering a new perspective on classical potential theory concepts.
Contribution
It provides a novel probabilistic approach to the Martin boundary construction, enhancing understanding and potentially simplifying existing methods.
Findings
Probabilistic construction of the Martin boundary
Maximal representing measures for positive harmonic functions
Enhanced intuition for potential theory concepts
Abstract
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.
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