{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:58:15Z","timestamp":1763978295136,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:00:00Z","timestamp":1664323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002848","name":"ANID-FONDECYT","doi-asserted-by":"publisher","award":["1201478","15110017"],"award-info":[{"award-number":["1201478","15110017"]}],"id":[{"id":"10.13039\/501100002848","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ANID\/FONDAP","award":["1201478","15110017"],"award-info":[{"award-number":["1201478","15110017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by \u039b(t)=|Z(t)|, where Z(t) is a stationary Gaussian process, is studied. Here, two particular cases are dealt with: (i) when the process Z(t) constitutes a family of independent random variables and with a common probability law N(0,1), and (ii) the case in which Z(t) is a second order stationary process, with exponential type covariance function. In these cases, we observe that the properties of the Gaussian process Z(t) are naturally transferred to the intensity \u039b(t) and that very analytical results are achievable from the analytical point of view for the point process N(t). Finally, some simulations are presented in order to appreciate what type of counting phenomena can be modeled by these cases of CP-FNI. In particular, it is interesting to see how the trajectories show a tendency of the events to be grouped in certain periods of time, also leaving long periods of time without the occurrence of events.<\/jats:p>","DOI":"10.3390\/axioms11100513","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T03:30:37Z","timestamp":1664335837000},"page":"513","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Temporal Cox Process with Folded Normal Intensity"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8046-6983","authenticated-orcid":false,"given":"Orietta","family":"Nicolis","sequence":"first","affiliation":[{"name":"Department of Engineering Sciences, Engineering Faculty, Universidad Andres Bello, Vi\u00f1a del Mar 2520000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis M.","family":"Riquelme Quezada","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Universidad de Santiago de Chile, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Germ\u00e1n","family":"Ibacache-Pulgar","sequence":"additional","affiliation":[{"name":"Institute of Statistics, University of Valparaiso, Valparaiso 2340000, Chile"},{"name":"Interdisciplinary Center for Atmospheric and Astro-Statistical Studies, University of Valparaiso, Valparaiso 2340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1111\/j.2517-6161.1955.tb00188.x","article-title":"Some statistical methods connected with series of events","volume":"17","author":"Cox","year":"1955","journal-title":"J. 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