Extremes of Moving Averages of Stable Processes
Extremes of Moving Averages of Stable Processes
复制标题
稳定过程的移动平均线的极值
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
H. Rootzén
中科院分区：
文献类型：
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作者：
H. Rootzén
摘要：研究了非正态稳定移动平均过程的极值问题。极值被描述为标记点过程，由（分离的）超过一个水平的点过程以及与点相关的标记组成，标记是X(t)在超过周围的归一化样本路径。证明了该标记点过程随着水平的增大在分布上收敛。极限分布是泊松过程的极限分布，泊松过程的独立标记具有随机的高度，但在其他方面是确定的。作为对连续时间情况的证明的副产品，得到了稳定过程的样本路径连续性的一个结果。
Abstract : In this paper extremes of non-normal stable moving average processes are studied. The extremes are described as a marked point process, consisting of the point process of (separated) exceedances of a level together with marks associated with the points, a mark being the normalized sample path of X(t) around an exceedance. It is proved that this marked point process converges in distribution as the level increases to infinity. The limiting distribution is that of a Poisson process with independent marks which have random heights but otherwise are deterministic. As a byproduct of the proof for the continuous-time case, a result on sample path continuity of stable processes is obtained.