{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T03:49:38Z","timestamp":1776743378428,"version":"3.51.2"},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T00:00:00Z","timestamp":1727913600000},"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":[[2025,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations which characterize nonlinear <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000627_inline1.png\"\/><jats:tex-math>\n$\\alpha$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-stable L\u00e9vy processes under a sublinear expectation space with <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000627_inline2.png\"\/><jats:tex-math>\n$\\alpha\\in(1,2)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We further establish the error bounds for the monotone approximation scheme. This in turn yields an explicit Berry\u2013Esseen bound and convergence rate for the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000627_inline3.png\"\/><jats:tex-math>\n$\\alpha$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-stable central limit theorem under sublinear expectation.<\/jats:p>","DOI":"10.1017\/jpr.2024.62","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T07:36:03Z","timestamp":1727940963000},"page":"209-233","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["On the rate of convergence for an \u03b1-stable central limit theorem under sublinear expectation"],"prefix":"10.1017","volume":"62","author":[{"given":"Mingshang","family":"Hu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lianzi","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0752-0773","authenticated-orcid":false,"given":"Gechun","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,10,3]]},"reference":[{"key":"S0021900224000627_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15007-4"},{"key":"S0021900224000627_ref13","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.2001.2014"},{"key":"S0021900224000627_ref16","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-23.1.179"},{"key":"S0021900224000627_ref5","first-page":"271","article-title":"Convergence of approximation schemes for fully nonlinear second order equations","volume":"4","author":"Barles","year":"1991","journal-title":"Asymp. Anal."},{"key":"S0021900224000627_ref3","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290343815X"},{"key":"S0021900224000627_ref7","doi-asserted-by":"publisher","DOI":"10.1137\/17M114995X"},{"key":"S0021900224000627_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-02000-5"},{"key":"S0021900224000627_ref21","volume-title":"Independent and Stationary Sequences of Random Variables","author":"Ibragimov","year":"1971"},{"key":"S0021900224000627_ref25","first-page":"639","article-title":"On the rate of convergence of finite-difference approximations for Bellman\u2019s equations","volume":"9","author":"Krylov","year":"1997","journal-title":"St. Petersburg Math. J."},{"key":"S0021900224000627_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139084659"},{"key":"S0021900224000627_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-004-0161-3"},{"key":"S0021900224000627_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70847-6_25"},{"key":"S0021900224000627_ref35","doi-asserted-by":"publisher","DOI":"10.1186\/s41546-019-0038-2"},{"key":"S0021900224000627_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-008-0160-z"},{"key":"S0021900224000627_ref38","doi-asserted-by":"publisher","DOI":"10.1214\/18-AAP1424"},{"key":"S0021900224000627_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2019.05.005"},{"key":"S0021900224000627_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s004400050264"},{"key":"S0021900224000627_ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-59903-7"},{"key":"S0021900224000627_ref29","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6656"},{"key":"S0021900224000627_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2019.08.005"},{"key":"S0021900224000627_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2020.124063"},{"key":"S0021900224000627_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02465818"},{"key":"S0021900224000627_ref17","doi-asserted-by":"crossref","unstructured":"[17] H\u00e4usler, E. and Luschgy, H. (2015). Stable Convergence and Stable Limit Theorems (Prob. Theory Stoch. Modelling 74), Springer, Cham.","DOI":"10.1007\/978-3-319-18329-9"},{"key":"S0021900224000627_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-012-0471-y"},{"key":"S0021900224000627_ref34","unstructured":"[34] Peng, S. (2008). A new central limit theorem under sublinear expectations. Preprint, arXiv:0803.2656."},{"key":"S0021900224000627_ref12","doi-asserted-by":"publisher","DOI":"10.1137\/15M1025530"},{"key":"S0021900224000627_ref1","unstructured":"[1] Arras, B. , Mijoule, G. , Poly, G. and Swan, Y. (2017). A new approach to the Stein\u2013Tikhomirov method: With applications to the second Wiener chaos and Dickman convergence. Preprint, arXiv:1605.06819."},{"key":"S0021900224000627_ref2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2002002"},{"key":"S0021900224000627_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.10.015"},{"key":"S0021900224000627_ref26","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v4-39"},{"key":"S0021900224000627_ref6","first-page":"2548","article-title":"An","volume":"22","author":"Bayraktar","year":"2016","journal-title":"Bernoulli"},{"key":"S0021900224000627_ref9","doi-asserted-by":"publisher","DOI":"10.1137\/090761501"},{"key":"S0021900224000627_ref8","doi-asserted-by":"publisher","DOI":"10.1142\/S0219891608001416"},{"key":"S0021900224000627_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2019.07.028"},{"key":"S0021900224000627_ref19","doi-asserted-by":"publisher","DOI":"10.3934\/puqr.2021001"},{"key":"S0021900224000627_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2024.03.013"},{"key":"S0021900224000627_ref15","first-page":"349","article-title":"Two-sided bounds on the rate of convergence to a stable law","volume":"57","author":"Hall","year":"1981","journal-title":"Prob. Theory Relat. Fields"},{"key":"S0021900224000627_ref14","doi-asserted-by":"publisher","DOI":"10.3150\/18-BEJ1063"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900224000627","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T13:45:55Z","timestamp":1743515155000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900224000627\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,3]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["S0021900224000627"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2024.62","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,3]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}