Authors: Natalia Markovich
Addresses: V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya str. 65, Moscow 117997, Russia
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. The 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 an asymptotically equivalent distribution and a limit expectation of the first hitting time to exceed the threshold un as the sample size n tends to infinity. The results can be extended to the second and, generally, to the kth (k > 2) hitting times. Applications in large-scale networks such as social, telecommunication and recommender systems are discussed.
Keywords: first hitting time; rare events; exceedance over threshold; cluster of exceedances; extremal index; application.
International Journal of Data Analysis Techniques and Strategies, 2017 Vol.9 No.4, pp.331 - 347
Received: 18 May 2016
Accepted: 22 Sep 2016
Published online: 30 Nov 2017 *