Two hypotheses on the exponential class in the class of O-subexponential infinitely divisible distributions

2019/12/18 by Toshiro Watanabe, Watanabe, Toshiro
Decision Sciences · Mathematics · #60E07 60G51 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #math.PR #msc:60E07 #msc:60G51

paper · pdf · doi:10.48550/arxiv.1912.08363

19 pages

arxiv created 2019/12/18 · openalex publication_date 2019/12/18 · arxiv updated 2019/12/19 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

Two hypotheses on the class L(γ) in the class OS∩ ID are discussed. Two weak hypotheses on the class L(γ) in the class OS∩ ID are proved. A necessary and sufficient condition in order that, for every t >0, the t-th convolution power of a distribution in the class OS∩ ID belongs to the class L(γ) is given.

Citations

• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)

Related

• Some positive conclusions related to the Embrechts-Goldie' conjecture
• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)
• Subexponentialiy of densities of infinitely divisible distributions
• Second order subexponentiality and infinite divisibility
• Two non-closure properties on the class of subexponential densities