Open Access
2019 Alternative constructions of a harmonic function for a random walk in a cone
Denis Denisov, Vitali Wachtel
Electron. J. Probab. 24: 1-26 (2019). DOI: 10.1214/19-EJP349


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 $C^{2}$.

Version Information

This article was first posted with a typographical error in one author's surname (Wachtel). The error was corrected on 13 November 2019.


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Denis Denisov. Vitali Wachtel. "Alternative constructions of a harmonic function for a random walk in a cone." Electron. J. Probab. 24 1 - 26, 2019.


Received: 3 May 2018; Accepted: 29 July 2019; Published: 2019
First available in Project Euclid: 12 September 2019

MathSciNet: MR4003145
Digital Object Identifier: 10.1214/19-EJP349

Primary: 60G50
Secondary: 60F17 , 60G40

Keywords: Exit time , Harmonic function , Random walk

Vol.24 • 2019
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