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[In Doney (Bull Lond Math Soc 19(2):177–182, 1987), R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalization of this factorization based on the theory recently developed for the exponential functional of Lévy processes. As a by-product, we provide some interesting distributional properties for these variables and also some new examples of the factorization of the arc-sine law.]
Published: Jul 30, 2021
Keywords: Lévy processes; arc-sine law; mellin transform; recurrence equation
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