Geodesic
Convex hulls of random walks: conic intrinsic volumes approach
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 159-171

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Sparre Andersen discovered a celebrated distribution-free formula for the probability of a random walk remaining positive up to a moment $n$. Kabluchko et al. expanded on this result by calculating the absorption probability for the convex hull of multidimensional random walks. They approached this by transforming the problem into a geometric one, which they then solved using Zaslavsky's theorem. We propose a completely different approach that allows us to directly derive the generating function for the absorption probability. The cornerstone of our method is the Gauss–Bonnet formula for polyhedral cones. 
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     author = {F. Petrov and J. Randon-Furling and D. Zaporozhets},
     title = {Convex hulls of random walks: conic intrinsic volumes approach},
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}
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F. Petrov; J. Randon-Furling; D. Zaporozhets. Convex hulls of random walks: conic intrinsic volumes approach. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 159-171. http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a9/