Alternative constructions of a harmonic function for a random walk in a cone

Denis Denisov; Vitali Wachtel

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arXiv · 1805.01437

Alternative constructions of a harmonic function for a random walk in a cone

Denis Denisov·Vitali Wachtel

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Abstract

For a random walk killed at leaving a cone we suggest two new constructions of a positive harmonic function. These constructions allow one to remove a quite strong extendability assumption, which has been imposed in our previous paper (Denisov and Wachtel, 2015, Random walks in cones). As a consequence, all the limit results from that paper remain true for cones which are either convex or star-like and $C^2$.

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Denis Denisov, Vitali Wachtel. 2018-05-03. Alternative constructions of a harmonic function for a random walk in a cone. https://arxiv.org/abs/1805.01437

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