逗留时间与脆弱性指数
Sojourn Times and the Fragility Index
摘要：
研究了连续随机过程Y在[0，1]上的高阈值以上的逗留时间.结果表明，当阈值增加时，如果Y对应的Copula过程处于极值过程的泛函吸引区域中，则存在期望逗留时间的极限（假定它是正的）。这个极限与对应于Y作为n的有限（n-）维分布的脆弱性指数的极限和阈值增加相一致。如果过程在广义Pareto过程的某个邻域内，则可以用一般的门限函数代替常数门限，计算出渐近的逗留时间逗留时间分布。极值过程就是一个突出的例子。假设在阈值以上的某个t_0处存在一个时间差，我们还可以计算过程在门限函数以上所花费的时间簇长度的渐近分布。
英文摘要：
We investigate the sojourn time above a high threshold of a continuous stochastic process Y on [0,1]. It turns out that the limit, as the threshold increases, of the expected sojourn time given that it is positive, exists if the copula process corresponding to Y is in the functional domain of attraction of of an extreme value process. This limit coincides with the limit of the fragility index corresponding to finite (n-)dimensional distributions of Y as n and the threshold increase. If the process is in a certain neighborhood of a generalized Pareto process, then we can replace the constant threshold by a general threshold function and we can compute the asymptotic sojourn time distribution. An extreme value process is a prominent example. Given that there is an exceedance at some t_0 above the threshold, we can also compute the asymptotic distribution of the time cluster length, which the process spends above the threshold function.
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