随机游动及相关Poisson过程的凹优数
Concave Majorants of Random Walks and Related Poisson Processes
摘要：
我们提供了一个统一的方法，理论的凹优的随机游动通过提供一个路径变换的有限长度的步行，离开法律的步行不变，同时提供完整的信息凹优。这导致了一个随机几何长度的步行描述为泊松点过程的游览远离其凹优，然后用来找到一个完整的描述凹优无限长的步行。在增量的子集可能有相同的算术平均的情况下，我们调查三个嵌套的组合物，自然产生于我们的建设凹优。
英文摘要：
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave majorant. This leads to a description of a walk of random geometric length as a Poisson point process of excursions away from its concave majorant, which is then used to find a complete description of the concave majorant for a walk of infinite length. In the case where subsets of increments may have the same arithmetic mean, we investigate three nested compositions that naturally arise from our construction of the concave majorant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
