{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T13:19:52Z","timestamp":1770556792516,"version":"3.49.0"},"reference-count":18,"publisher":"IOP Publishing","issue":"12","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"crossref","award":["19805\/2014."],"award-info":[{"award-number":["19805\/2014."]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["28177\/2017"],"award-info":[{"award-number":["28177\/2017"]}]},{"DOI":"10.13039\/501100006753","name":"Centro de Matem\u00e1tica Universidade do Porto","doi-asserted-by":"crossref","award":["00144\/2013"],"award-info":[{"award-number":["00144\/2013"]}],"id":[{"id":"10.13039\/501100006753","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2019,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    When there is no independence, abnormal observations may have a tendency to appear in clusters instead of being scattered along the time frame. Identifying clusters and estimating their size are important problems arising in the statistics of extremes or in the study of quantitative recurrence for dynamical systems. In the classical literature, the extremal index appears to be linked to the cluster size and, in fact, it is usually interpreted as the reciprocal of the mean cluster size. This quantity involves a passage to the limit and in some special cases this interpretation fails due to an escape of mass when computing limiting point processes. Smith (1988\n                    <jats:italic>Adv. Appl. Probab<\/jats:italic>\n                    .\n                    <jats:bold>20<\/jats:bold>\n                    681\u20133), introduced a regenerative process exhibiting such disagreement. Very recently, in Abadi (2018 (arXiv:1808.02970)) the authors used a dynamical mechanism to emulate the same inadequacy of the usual interpretation of the extremal index. Here, we consider a general regenerative process that includes Smith\u2019s model, show that it is important to consider finite time quantities instead of asymptotic ones and compare their different behaviours in relation to the cluster size. We consider other indicators, such as what we call the sojourn time, which corresponds to the size of groups of abnormal observations, when there is some uncertainty regarding where the cluster containing that group was actually initiated. We also study the decay of correlations of the non-Markovian models considered.\n                  <\/jats:p>","DOI":"10.1088\/1361-6544\/ab37b8","type":"journal-article","created":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T12:13:29Z","timestamp":1572351209000},"page":"4853-4870","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Clustering indices and decay of correlations in non-Markovian models"],"prefix":"10.1088","volume":"32","author":[{"given":"Miguel","family":"Abadi","sequence":"first","affiliation":[]},{"given":"Ana Cristina Moreira","family":"Freitas","sequence":"additional","affiliation":[]},{"given":"Jorge Milhazes","family":"Freitas","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"nonab37b8bib001","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1007\/s00574-006-0030-1","type":"journal-article","article-title":"Hitting, returning and the short correlation function","volume":"37","author":"Abadi","year":"2006","journal-title":"Bull. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2018-12-20","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-08-01","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-10-29","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}