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Journal Articles Annales Henri Lebesgue Year : 2022

Martin boundary of random walks in convex cones

Abstract

We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique positive discrete harmonic function for these processes (up to a multiplicative constant); in other words, the Martin boundary reduces to a singleton.
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Dates and versions

hal-02499786 , version 1 (05-03-2020)

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Jetlir Duraj, Kilian Raschel, Pierre Tarrago, Vitali Wachtel. Martin boundary of random walks in convex cones. Annales Henri Lebesgue, 2022, 5, pp.559-609. ⟨10.5802/ahl.130⟩. ⟨hal-02499786⟩
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