The convex minorant of a Lévy process
The convex minorant of a Lévy process
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Lévy 过程的凸短矩
DOI：
10.1214/11-aop658
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发表时间：
2010
影响因子：
2.3
通讯作者：
Gerónimo Uribe Bravo
中科院分区：
文献类型：
--
作者：
J. Pitman;Gerónimo Uribe Bravo
我们为具有连续分布的Levy过程的凸亚微商理论提供了统一的方法。新的结果包括在有限和无限时间区间上的Levy过程的凸次子集的简单的显式构造，以及凸次子集上直到独立指数时间的游程的泊松点过程的简单显式构造。证明了参数为1的Poisson-Dirichlet分布是区间[0，1]上凸次亚群上连续分布的Levy过程的游程长度的普遍规律.
We offer a unified approach to the theory of convex minorants of Levy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a Levy process on both finite and infinite time intervals, and of a Poisson point process of excursions above the convex minorant up to an independent exponential time. The Poisson–Dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a Levy process with continuous distributions above its convex minorant on the interval [0,1].