Some positive conclusions related to the Embrechts-Goldie' conjecture

2016/09/04 by Yuebao Wang, Wang, Yuebao, Zhaolei Cui +3
Mathematics · #60E05 #60F10 #60G50 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E05 #msc:60F10 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1609.00912

22 pages

arxiv created 2017/07/30 · arxiv updated 2017/08/01

Abstract

In this paper, we give some conditions, under which, if an infinitely divisible distribution supported on [0,∞) belongs to the intersection of exponential distribution class L(γ) for some γ≥0 and generalised subexponential distribution class OS, then its L\rm\acuteevy spectral distribution or convolution of the distribution with itself also belongs to the same one. To this end, we discuss the closure under the compound convolution roots for the class. In addition, we do some in-depth discussion about the above-mentioned conditions, and provide some types of distributions satisfying them. Further, we obtain some local versions of the above-mentioned results by the Esscher transform of distributions. Therefore, some positive conclusions related to the Embrechts-Goldie conjecture are obtained. Prior to this, all corresponding results are negative

Related

• The conjectures of Embrechts and Goldie
• Two hypotheses on the exponential class in the class of O-subexponential infinitely divisible distributions
• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)
• The class \boldsymbolQ and mixture distributions with dominated continuous singular parts
• New Classes of Infinitely Divisible Distributions Related to the Goldie-Steutel-Bondesson Class