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

2018/05/03 by Denis Denisov, Denisov, Denis, Vitali Wachtel +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1805.01437

openalex publication_date 2018/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a random walk killed at leaving a cone we suggest two new constructions\nof a positive harmonic function. These constructions allow one to remove a\nquite strong extendability assumption, which has been imposed in our previous\npaper (Denisov and Wachtel, 2015, Random walks in cones). As a consequence, all\nthe limit results from that paper remain true for cones which are either convex\nor star-like and C².\n

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