Abstract In this work, we refine the results of Sendov and Shan [New representation theorems for completely monotone and Bernstein functions with convexity properties on their measures, J. Theor. Probab. 28 (2015), 1689–1725] on subordinators obtained by the class of Bernstein functions stable by the Mellin-Euler differential operator I − x d d x I-x\tfrac{\text{d}}{\text{d}x} by giving a stochastic interpretation, proving monotonicity properties of the related distributions and providing additional extensions.

中文翻译：

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三类可分解分布

摘要 在这项工作中，我们改进了 Sendov 和 Shan [新表示定理的完全单调和 Bernstein 函数在其度量上具有凸性属性，J. Theor。可能。28 (2015), 1689–1725] 关于由梅林-欧拉微分算子 I − xddx Ix\tfrac{\text{d}}{\text{d}x} 通过给出一个随机解释，证明相关分布的单调性并提供额外的扩展。