A Sufficient Condition for Absolute Continuity of Infinitely Divisible Distributions

2016/06/11 by Kasra Alishahi, Alishahi, Kasra, Erfan Salavati +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60E07 #60G51 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1606.07106

openalex publication_date 2016/06/11 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

We consider infinitely divisible distributions with symmetric Lévy measure and study the absolute continuity of them with respect to the Lebesgue measure. We prove that if η(r)=∫_{|x|≤ r} x² ν(dx) where ν is the Lévy measure, then ∫₀¹ (r)/(η(r))dr

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