{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:41Z","timestamp":1740165281001,"version":"3.37.3"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,17]],"date-time":"2024-02-17T00:00:00Z","timestamp":1708128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"In this paper, we investigate an application of the statistical concept of causality, based on Granger\u2019s definition of causality, on raw increasing processes as well as on optional and predictable measures. A raw increasing process is optional (predictable) if the bounded (left-continuous) process X, associated with the measure \u03bcA(X), is self-caused. Also, the measure \u03bcA(X) is optional (predictable) if an associated process X is self-caused with some additional assumptions. Some of the obtained results, in terms of self-causality, can be directly applied to defining conditions for an optional stopping time to become predictable.<\/jats:p>","DOI":"10.3390\/axioms13020124","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T08:18:38Z","timestamp":1708330718000},"page":"124","source":"Crossref","is-referenced-by-count":0,"title":["Application of the Concept of Statistical Causality in Integrable Increasing Processes and Measures"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1652-9983","authenticated-orcid":false,"given":"Dragana","family":"Valjarevi\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia"},{"name":"Faculty of Education, University of East Sarajevo, 76300 Bijeljina, Bosnia and Herzegovina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3819-4387","authenticated-orcid":false,"given":"Vladica","family":"Stojanovi\u0107","sequence":"additional","affiliation":[{"name":"Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11080 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2997-2164","authenticated-orcid":false,"given":"Aleksandar","family":"Valjarevi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Geography, University of Belgrade, 11000 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,17]]},"reference":[{"key":"ref_1","unstructured":"Bohm, D. 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[Ph.D. Thesis, Department of Mathematical and Statistical Sciences, University of Alberta]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/124\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T08:55:27Z","timestamp":1708332927000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,17]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["axioms13020124"],"URL":"https:\/\/doi.org\/10.3390\/axioms13020124","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,2,17]]}}}