Concave Majorants of Random Walks and Related Poisson Processes
Concave Majorants of Random Walks and Related Poisson Processes
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随机游走的凹主函数及相关泊松过程
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Pitman
中科院分区：
文献类型：
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作者：
Joshua Abramson;J. Pitman
我们为随机游走的凹主频理论提供了一种统一的方法，通过为有限长度的游走提供路径变换，使游走定律保持不变，同时提供有关凹主频的完整信息。这导致将随机几何长度的游走描述为远离其凹主波的泊松点过程，然后使用该泊松点过程来找到无限长度游走的凹主波的完整描述。在增量子集可能具有相同算术平均值的情况下，我们研究了三个嵌套组合，这些组合自然是由我们构建凹主函数而产生的。
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 of 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.