论文标题
一系列高斯流程的一系列趋势过程的极端价值理论
Extreme value theory for a sequence of suprema of a class of Gaussian processes with trend
论文作者
论文摘要
我们研究了一类随机序列的极端价值理论，这些序列由趋势的汇总自相似过程的历史上的跨越跨度定义。这项研究是由于其在各个领域的潜在应用及其理论上的兴趣而动机。我们考虑通过考虑趋势功能是否相同的固定序列和非平稳序列。我们表明，根据模型参数所分配的三种条件，一系列适当归一化的$ K $ th订单统计量会收敛于分布的分布到限制随机变量。值得注意的是，这种现象类似于固定正常序列。我们还表明，标准化的$ K $ TH订单统计信息的各种矩会收敛到相应限制随机变量的矩。获得的结果使我们能够分析这些随机序列的各种特性，从而揭示了这类随机序列在极值理论中的有趣特殊性。
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its theoretical interestingness. We consider both stationary sequences and non-stationary sequences obtained by considering whether the trend functions are identical or not. We show that a sequence of suitably normalised $k$th order statistics converges in distribution to a limiting random variable which can be a negative log transformed Erlang distributed random variable, a Normal random variable or a mixture of them, according to three conditions deduced through the model parameters. Remarkably, this phenomenon resembles that for the stationary Normal sequence. We also show that various moments of the normalised $k$th order statistics converge to the moments of the corresponding limiting random variable. The obtained results enable us to analyze various properties of these random sequences, which reveals the interesting particularities of this class of random sequences in extreme value theory.
