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Self-Standardized Central Limit Theorems for Trimmed Lévy Processes
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2020-07-14 , DOI: 10.1007/s10959-020-01021-0
David M. Mason

We prove under general conditions that a trimmed subordinator satisfies a self-standardized central limit theorem (SSCLT). Our basic tool is a powerful distributional approximation result of Zaitsev (Probab Theory Relat Fields 74:535–566, 1987). Among other results, we obtain as special cases of our subordinator result the recent SSCLTs of Ipsen et al. (Stoch Process Appl 130:2228–2249, 2020) for trimmed subordinators and a trimmed subordinator analog of a central limit theorem of Csorgő et al. (Probab Theory Relat Fields 72:1–16, 1986) for intermediate trimmed sums in the domain of attraction of a stable law. We then use our methods to prove a similar theorem for general Levy processes.

中文翻译:

修整 Lévy 过程的自标准化中心极限定理

我们在一般条件下证明修剪的从属满足自标准化中心极限定理(SSCLT)。我们的基本工具是 Zaitsev (Probab Theory Relat Fields 74:535–566, 1987) 的强大分布近似结果。在其他结果中,我们获得了 Ipsen 等人最近的 SSCLT 作为我们的下级结果的特殊情况。(Stoch Process Appl 130:2228–2249, 2020) 用于修整从属子和 Csorgő 等人的中心极限定理的修整从属子类比。(Probab Theory Relat Fields 72:1–16, 1986)用于稳定定律的吸引力域中的中间修整和。然后我们使用我们的方法来证明一般 Levy 过程的类似定理。
更新日期:2020-07-14
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