{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T16:25:16Z","timestamp":1776270316372,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T00:00:00Z","timestamp":1700524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["Researchers Supporting Project number (RSPD2023R1075)"],"award-info":[{"award-number":["Researchers Supporting Project number (RSPD2023R1075)"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the It\u00f4\u2013Krylov\u2019s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts.<\/jats:p>","DOI":"10.3390\/axioms12121068","type":"journal-article","created":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T03:54:37Z","timestamp":1700625277000},"page":"1068","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0889-3387","authenticated-orcid":false,"given":"Mhamed","family":"Eddahbi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1420-2071","authenticated-orcid":false,"given":"Omar","family":"Kebiri","sequence":"additional","affiliation":[{"name":"Department of Stochastics and Its Applications, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, 03046 Cottbus, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abou","family":"Sene","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gaston Berger University, Saint Louis B.P. 234, Senegal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bismut, J.M. (1978). 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