Convex minorants of random walks and Lévy processes
Convex minorants of random walks and Lévy processes
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随机游走和 Lévy 过程的凸辅子
DOI：
10.1214/ecp.v16-1648
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发表时间：
2011
影响因子：
0.5
通讯作者：
Gerónimo Uribe Bravo
中科院分区：
文献类型：
--
作者：
Joshua Abramson;J. Pitman;Nathan Ross;Gerónimo Uribe Bravo
本文概述了最近关于随机漫步和Levy过程的凸小量的描述和性质的工作，总结和扩展了这些主题的文献。研究结果包括随机漫步和Levy过程在固定有限区间、独立指数时间和无限视界情况下的凸小量的点过程描述。这些描述来自于这些过程在适当的路径变换下的不变性。在布朗运动的情况下，我们注意到该过程的进一步特殊性质，包括时间反转，如何暗示布朗弯曲的凸小量的顺序描述。
This article provides an overview of recent work on descriptions and properties of the Convex minorants of random walks and Levy processes, which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and Levy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.