{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:32:36Z","timestamp":1760059956220,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901058","2021CFB543"],"award-info":[{"award-number":["11901058","2021CFB543"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["11901058","2021CFB543"],"award-info":[{"award-number":["11901058","2021CFB543"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper examines temporal symmetry breaking and structural duality in a class of time-changed McKean\u2013Vlasov neutral stochastic differential equations. The system features super-linear drift coefficients satisfying a one-sided local Lipschitz condition and incorporates a fundamental duality: one drift component evolves under a random time change Et, while the other progresses in regular time t. Within the symmetric framework of mean-field interacting particle systems, where particles exhibit permutation invariance, we establish strong convergence of the tamed Euler\u2013Maruyama method over finite time intervals. By replacing the one-sided local condition with a globally symmetric Lipschitz assumption, we derive an explicit convergence rate for the numerical scheme. Two numerical examples validate the theoretical results.<\/jats:p>","DOI":"10.3390\/sym17081178","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T14:22:44Z","timestamp":1753280564000},"page":"1178","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Tamed Euler\u2013Maruyama Method of Time-Changed McKean\u2013Vlasov Neutral Stochastic Differential Equations with Super-Linear Growth"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6080-2692","authenticated-orcid":false,"given":"Jun","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1239\/jap\/1091543414","article-title":"Limit theorems for continuous-time random walks with infinite mean waiting times","volume":"41","author":"Meerschaert","year":"2004","journal-title":"J. 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