{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:26:21Z","timestamp":1787541981758,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100011002","name":"National Natural Science Foundation of China-Yunnan Joint Fund","doi-asserted-by":"publisher","award":["11771158"],"award-info":[{"award-number":["11771158"]}],"id":[{"id":"10.13039\/501100011002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["170137"],"award-info":[{"award-number":["170137"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003190","name":"Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universit\u00c3\u00a4t Freiburg","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are directly connected to the representation of solutions to backward stochastic differential equations. The proposed scheme is based on splitting the equation into two parts, the first corresponding to a linear parabolic equation and the second to a Hamilton--Jacobi equation. The solutions of these two equations are approximated using, respectively, the Feynman--Kac and the Hopf--Lax formula. We establish the convergence of the scheme and determine the convergence rate, combining Krylov's shaking coefficients technique and the Barles--Jakobsen optimal switching approximation.<\/jats:p>","DOI":"10.1137\/18m1198831","type":"journal-article","created":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T10:11:21Z","timestamp":1578564681000},"page":"165-191","source":"Crossref","is-referenced-by-count":8,"title":["An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians"],"prefix":"10.1137","volume":"58","author":[{"given":"Shuo","family":"Huang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0752-0773","authenticated-orcid":true,"given":"Gechun","family":"Liang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thaleia","family":"Zariphopoulou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,1,9]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290343815X"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-02000-5"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2002002"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-1991-4305"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/num.21841"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/08073041X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-014-9255-3"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.01.001"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20208"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1090"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-018-0377-3"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-010-0271-1"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00093"},{"key":"atypb14","unstructured":"L. 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Huang,\n                      An Approximation Scheme for Variational Inequalities with Convex and Coercive Hamiltonians\n                      , working paper,arXiv:1810.08842, 2018."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202503002660"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1019160253"},{"key":"atypb24","first-page":"639","volume":"9","author":"Krylov N. V.","year":"1997","journal-title":"St. Petersburg Math. J."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/s004400050264"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2015.1029074"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/0716071"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/14.1.113"},{"key":"atypb29","first-page":"169","volume":"460","author":"Lyons T.","year":"2004","journal-title":"Proc. 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