Electronic Communications in Probability

On harmonic functions of killed random walks in convex cones

Jetlir Duraj

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Abstract

We prove the existence of uncountably many nonnegative harmonic functions for random walks in the euclidean space with non-zero drift, killed when leaving general convex cones with vertex in 0. We also make the natural conjecture about the Martin boundary for lattice random walks in general convex cones in two dimensions. Proving that the set of harmonic functions found is the full Martin boundary for these processes is an open problem.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 80, 10 pp.

Dates
Accepted: 17 November 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316782

Digital Object Identifier
doi:10.1214/ECP.v19-3219

Mathematical Reviews number (MathSciNet)
MR3283611

Zentralblatt MATH identifier
1325.60068

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J50: Boundary theory

Keywords
killed random walk harmonic functions Martin boundary

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Duraj, Jetlir. On harmonic functions of killed random walks in convex cones. Electron. Commun. Probab. 19 (2014), paper no. 80, 10 pp. doi:10.1214/ECP.v19-3219. https://projecteuclid.org/euclid.ecp/1465316782


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