Sojourn times and the fragility index

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Falk, Michael¹  Hofmann, Martin¹ 

[1] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

关键词: Sojourn time;    Fragility index;    Max-stable process;    Functional domain of attraction;    Copula process;    Generalized Pareto process;    Expected shortfall;    Sojourn time distribution;    Excursion time;   

DOI  :  10.1016/j.spa.2011.11.009

来源: Elsevier

【 摘 要 】

We investigate the sojourn time above a high threshold of a continuous stochastic process Y = (Y-t)(t is an element of[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 a max-stable process. This limit coincides with the limit of the fragility index corresponding to (Y-i/n)(1 <= i <= n) 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. A max-stable process is a prominent example. Given that there is an exceedance at to above the threshold, we can also compute the asymptotic distribution of the excursion time, which the process spends above the threshold function. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free