{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T02:06:29Z","timestamp":1775527589391,"version":"3.50.1"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We prove a scaling limit theorem for two-type Galton\u2013Watson branching processes with interaction. The limit theorem gives rise to a class of mixed-state branching processes with interaction used to simulate evolution for cell division affected by parasites. Such processes can also be obtained by the pathwise-unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability 1 and the exponential ergodicity in the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225100284_inline1.png\"\/>\n                        <jats:tex-math>$L^1$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -Wasserstein distance of such processes in some cases.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.10028","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T10:26:06Z","timestamp":1759141566000},"page":"135-156","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Mixed-state branching evolution for cell division models"],"prefix":"10.1017","volume":"63","author":[{"given":"Shukai","family":"Chen","sequence":"first","affiliation":[{"name":"Fujian Normal University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3739-2891","authenticated-orcid":false,"given":"Lina","family":"Ji","sequence":"additional","affiliation":[{"name":"Shenzhen MSU-BIT University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Xiong","sequence":"additional","affiliation":[{"name":"Southern University of Science and Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,9,29]]},"reference":[{"key":"S0021900225100284_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2018.09.003"},{"key":"S0021900225100284_ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2023.104262"},{"key":"S0021900225100284_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOP629"},{"key":"S0021900225100284_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15004-3"},{"key":"S0021900225100284_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65371-1"},{"key":"S0021900225100284_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10473-021-0504-7"},{"key":"S0021900225100284_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(95)00055-0"},{"key":"S0021900225100284_ref17","doi-asserted-by":"publisher","DOI":"10.1134\/S008154382201014X"},{"key":"S0021900225100284_ref16","unstructured":"[16] Ikeda, N. and Watanabe, S. (1981). Stochastic Differential Equations and Diffusion Processes, 2nd edn. North-Holland, Amsterdam."},{"key":"S0021900225100284_ref3","first-page":"95","article-title":"Branching Feller diffusion for cell division with parasite infection","volume":"8","author":"Bansaye","year":"2011","journal-title":"ALEA, Lat. Am. J. Prob. Math. Statist."},{"key":"S0021900225100284_ref18","doi-asserted-by":"publisher","DOI":"10.1137\/1116003"},{"key":"S0021900225100284_ref32","unstructured":"[32] Osorio, L. and Winter, A. (2020). Two-level branching model for virus population under cell division. Preprint, arXiv:2004.14352."},{"key":"S0021900225100284_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71050-9"},{"key":"S0021900225100284_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/20-EJP528"},{"key":"S0021900225100284_ref26","doi-asserted-by":"crossref","unstructured":"[26] Li, Z. (2020). Continuous-state branching processes with immigration. In From Probability to Finance: Mathematical Lectures from Peking University, ed. Y. Jiao. 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(1992). Lectures on the Coupling Method. John Wiley, New York."},{"key":"S0021900225100284_ref5","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1222441825"},{"key":"S0021900225100284_ref24","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1143936261"},{"key":"S0021900225100284_ref14","doi-asserted-by":"publisher","DOI":"10.30757\/ALEA.v20-22"},{"key":"S0021900225100284_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-37632-0"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100284","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:25:29Z","timestamp":1775525129000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100284\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,29]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0021900225100284"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10028","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,29]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. 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