Subexponential densities of compound Poisson sums and the supremum of a random walk

2020/01/29 by Shimura, Takaaki, Watanabe, Toshiro
#60E07 #60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2001.11362

Abstract

We characterize the subexponential densities on (0,∞) for compound Poisson distributions on [0,∞) with absolutely continuous Lévy measures. As a corollary, we show that the class of all subexponential probability density functions on \mathbb R₊ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on (0,∞) for the distribution of the supremum of a random walk.

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