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Recently, the case where the times of immigration are generated by a non-homogeneous Poisson process has been considered in depth. In this work, we demonstrate how we can use the framework of point processes in order to go beyond the Poisson process. As an illustration, we show how to transfer techniques from the case of Poisson immigration to the case where it is spanned by a determinantal point process.<\/jats:p>","DOI":"10.1017\/jpr.2025.10059","type":"journal-article","created":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T12:18:51Z","timestamp":1768220331000},"page":"828-848","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Multitype branching processes with immigration generated by point processes"],"prefix":"10.1017","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1647-9338","authenticated-orcid":false,"given":"Martin","family":"Minchev","sequence":"first","affiliation":[{"name":"Sofia University \u2018St. Kliment Ohridski\u2019"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8832-7336","authenticated-orcid":false,"given":"Maroussia","family":"Slavtchova-Bojkova","sequence":"additional","affiliation":[{"name":"Sofia University \u2018St. Kliment Ohridski\u2019 and Bulgarian Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,12]]},"reference":[{"key":"S0021900225100594_ref23","volume-title":"Lectures on the Poisson Process","author":"Last","year":"2018"},{"key":"S0021900225100594_ref7","doi-asserted-by":"publisher","DOI":"10.1134\/S000143461211003X"},{"key":"S0021900225100594_ref4","unstructured":"[4] Badalbaev, I. and Rahimov, I. 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