{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T15:00:39Z","timestamp":1773932439570,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["16K00160"],"award-info":[{"award-number":["16K00160"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It has been clarified that words in written texts are classified into two groups called Type-I and Type-II words. The Type-I words are words that exhibit long-range dynamic correlations in written texts while the Type-II words do not show any type of dynamic correlations. Although the stochastic process of yielding Type-II words has been clarified to be a superposition of Poisson point processes with various intensities, there is no definitive model for Type-I words. In this study, we introduce a Hawkes process, which is known as a kind of self-exciting point process, as a candidate for the stochastic process that governs yielding Type-I words; i.e., the purpose of this study is to establish that the Hawkes process is useful to model occurrence patterns of Type-I words in real written texts. The relation between the Hawkes process and an existing model for Type-I words, in which hierarchical structures of written texts are considered to play a central role in yielding dynamic correlations, will also be discussed.<\/jats:p>","DOI":"10.3390\/e24070858","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T21:31:06Z","timestamp":1655933466000},"page":"858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling Long-Range Dynamic Correlations of Words in Written Texts with Hawkes Processes"],"prefix":"10.3390","volume":"24","author":[{"given":"Hiroshi","family":"Ogura","sequence":"first","affiliation":[{"name":"Department of Information Science, Faculty of Arts and Sciences, Showa University, Fujiyoshida 403-0005, Japan"}]},{"given":"Yasutaka","family":"Hanada","sequence":"additional","affiliation":[{"name":"Department of Information Science, Faculty of Arts and Sciences, Showa University, Fujiyoshida 403-0005, Japan"}]},{"given":"Hiromi","family":"Amano","sequence":"additional","affiliation":[{"name":"Department of Information Science, Faculty of Arts and Sciences, Showa University, Fujiyoshida 403-0005, Japan"}]},{"given":"Masato","family":"Kondo","sequence":"additional","affiliation":[{"name":"Department of Information Science, Faculty of Arts and Sciences, Showa University, Fujiyoshida 403-0005, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1080\/09296179708590097","article-title":"Time-Series Analysis in Linguistics. 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