The extremal index of a higher-order stationary Markov chain

• 成果类型: Article
• 署名作者: Yun, S
• 署名单位: Suwon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 408-437
• 关键词: value distributions; SEQUENCES; events

摘要

The paper presents a method of computing the extremal index of a real-valued, higher-order (kth-order, k greater than or equal to 1) stationary Markov chain (X-n). The method is based on the assumption that the joint distribution of k + 1 consecutive variables is in the domain of attraction of some multivariate extreme value distribution. We introduce limiting distributions of some rescaled stationary transition kernels, which are used to define a new (k - 1)th-order Markov chain (Y-n), say. Then, the kth-order Markov chain (Z(n)) defined by Z(n) = Y-1+...+ Y-n is used to derive a representation for the extremal index of (X-n). We further establish convergence in distribution of multilevel exceedance point processes for (X-n) in terms of (Z(n)). The representations for the extremal index and for quantities characterizing the distributional limits are well suited for Monte Carlo simulation.