Electronic Communications in Probability

On harmonic functions of killed random walks in convex cones

Jetlir Duraj

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

killed random walk harmonic functions Martin boundary

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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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