Hitting times of threshold exceedances and their distributions

2015/01/07 by Natalia M. Markovich, Natalia Markovich, Markovich, Natalia
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1501.01561

6 pages, International Conference on Risk Analysis ICRA 6 / RISK 2015 Barcelona, May 26 - 29, 2015

arxiv created 2015/01/07 · openalex publication_date 2015/01/07 · arxiv updated 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to dependence such exceedances tend to occur in clusters. Cluster structure of social networks is caused by dependence (social relationships and interests) between nodes and possibly heavy-tailed distributions of the node degrees. A minimal time to reach a large node determines the first hitting time. We derive asymptotically equivalent distribution and a limit expectation of the first hitting time to exceed the threshold u_n as sample size n tends to infinity. The results can be extended to the second and, generally, to kth (k>2) hitting times.

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