The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
复制标题
具有规则变化的跳跃大小分布的随机游走的最大增量的极限分布
DOI：
10.3150/10-bej255
复制
发表时间：
2010
期刊：
影响因子：
1.5
通讯作者：
Alfredas Ravckauskas
中科院分区：
文献类型：
--
作者：
T. Mikosch;Alfredas Ravckauskas
在本文中，我们处理了一个跳跃大小有规则变化的随机漫步的最大增量的渐近分布。这一问题是由长期存在的流行病替代品的变化点检测问题引起的。结果表明，随机漫步的最大增量的极限分布是经典的极值分布之一，即Frechet分布。我们在点过程的一般框架下证明了在可分离的Banach空间中跳跃大小取值的结果。
In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic alternatives. It turns out that the limit distribution of the maximum increment of the random walk is one of the classical extreme value distributions, the Frechet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space.