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

Abstract

Two hypotheses on the class $\mathcal{L}(\gamma )$ in the class $\mathcal{O}\mathcal{S}\cap \mathcal{I}\mathcal{D}$ are discussed. Two weak hypotheses on the class $\mathcal{L}(\gamma )$ in the class $\mathcal{O}\mathcal{S}\cap \mathcal{I}\mathcal{D}$ 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 $\mathcal{O}\mathcal{S}\cap \mathcal{I}\mathcal{D}$ belongs to the class $\mathcal{L}(\gamma )$ is given.

19 pages

References in corpus (2)

• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)
• Some positive conclusions related to the Embrechts-Goldie' conjecture