{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T10:54:03Z","timestamp":1776336843264,"version":"3.51.2"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Public Scholarship, Development, Disability and Maintenance Fund of the Republic of Slovenia"},{"DOI":"10.13039\/100012338","name":"Alan Turing Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006734","name":"Princeton University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006734","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/S026347\/1"],"award-info":[{"award-number":["EP\/S026347\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V026259\/1"],"award-info":[{"award-number":["EP\/V026259\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N5101"],"award-info":[{"award-number":["EP\/N5101"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["OobfJ22\\100020"],"award-info":[{"award-number":["OobfJ22\\100020"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000835","name":"University of Bath","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000835","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2025,12,31]]},"DOI":"10.1137\/23m161077x","type":"journal-article","created":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T09:00:37Z","timestamp":1759482037000},"page":"1541-1567","source":"Crossref","is-referenced-by-count":1,"title":["Generative Modeling of L\u00e9vy Area for High Order SDE Simulation"],"prefix":"10.1137","volume":"7","author":[{"given":"Andra\u017e","family":"Jelin\u010di\u010d","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK."}]},{"given":"Jiajie","family":"Tao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College London, London WC1E 6BT, UK."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1043-6129","authenticated-orcid":true,"given":"William F.","family":"Turner","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK."}]},{"given":"Thomas","family":"Cass","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK."},{"name":"Institute for Advanced Study, Princeton, NJ 18540 USA."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6403-4993","authenticated-orcid":true,"given":"James","family":"Foster","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK."}]},{"given":"Hao","family":"Ni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College London, London WC1E 6BT, UK."}]}],"member":"351","published-online":{"date-parts":[[2025,10,3]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"20200652","DOI":"10.1098\/rsif.2020.0652","volume":"17","author":"Browning A.","year":"2020","journal-title":"J. R. Soc. Interface"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2307\/1969671","volume":"65","author":"Chen K.-T.","year":"1957","journal-title":"Ann. Math."},{"key":"ref3","doi-asserted-by":"crossref","first-page":"4049","DOI":"10.1214\/15-AOP1068","volume":"44","author":"Chevyrev I.","year":"2016","journal-title":"Ann. Probab."},{"key":"ref4","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/BFb0004007","volume-title":"Stochastic Differential Systems Filtering and Control","author":"Clark J. M. C.","year":"1980"},{"key":"ref6","series-title":"Springer Proc. Math. Statist. 100","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-3-319-11292-3_7","volume-title":"Stochastic Analysis and Applications 2014","author":"Davie A.","year":"2014"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1080\/07362990701540592","volume":"25","author":"Dickinson A. S.","year":"2007","journal-title":"Stoch. Anal. Appl."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/23M155147X"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1017\/S096354832200030X","volume":"32","author":"Foster J.","year":"2023","journal-title":"Combin. Probab. Comput."},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/19M1261912"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139992235706"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1287\/opre.1070.0496","volume":"56","author":"Giles M. B.","year":"2008","journal-title":"Oper. Res."},{"key":"ref17","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1214\/13-AAP957","volume":"24","author":"Giles M. B.","year":"2014","journal-title":"Ann. Appl. Probab."},{"key":"ref18","volume-title":"Advances in Neural Information Processing Systems","volume":"27","author":"Goodfellow I.","year":"2014"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s11075-022-01401-z","volume":"93","author":"Kastner F.","year":"2023","journal-title":"Numer. Algorithms"},{"key":"ref22","first-page":"18747","volume-title":"Advances in Neural Information Processing Systems","volume":"34","author":"Kidger P.","year":"2021"},{"key":"ref24","series-title":"Appl. Math. (N. Y.), 23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12616-5","volume-title":"Numerical Solution of Stochastic Differential Equations","author":"Kloeden P.","year":"1992"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1080\/07362999208809281","volume":"10","author":"Kloeden P.","year":"1992","journal-title":"Stoch. Anal. Appl."},{"key":"ref26","series-title":"Interdiscip. Appl. Math.,\u00a039","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-16375-8","volume-title":"Molecular Dynamics: With Deterministic and Stochastic Numerical Methods","author":"Leimkuhler B.","year":"2015"},{"key":"ref27","first-page":"217","volume-title":"Advances in Neural Information Processing Systems","volume":"33","author":"Li S.","year":"2020"},{"key":"ref29","volume-title":"Advances in Neural Information Processing Systems","author":"Li X.","year":"2019"},{"key":"ref30","series-title":"Grad. Texts in Math. 46","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6257-2","volume-title":"Probability Theory","author":"Lo\u00e8ve M.","year":"1978","edition":"4"},{"key":"ref31","first-page":"39755","volume-title":"Advances in Neural Information Processing Systems","volume":"36","author":"Lou H.","year":"2023"},{"key":"ref32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71285-5","volume-title":"Differential Equations Driven by Rough Paths","author":"Lyons T. J.","year":"2007"},{"key":"ref33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10063-9","volume-title":"Stochastic Numerics for Mathematical Physics","author":"Milstein G. N.","year":"2004"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1080\/07362994.2021.1922291","volume":"40","author":"Mrongowius J.","year":"2022","journal-title":"Stoch. Anal. Appl."},{"key":"ref37","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s00780-009-0101-4","volume":"13","author":"Ninomiya M.","year":"2009","journal-title":"Finance Stoch."},{"key":"ref38","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/13504860701413958","volume":"15","author":"Ninomiya S.","year":"2008","journal-title":"Appl. Math. Finance"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF01438265","volume":"3","author":"Pardoux E.","year":"1985","journal-title":"Acta Appl. Math."},{"key":"ref40","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1137\/060673308","volume":"47","author":"R\u00f6ler A.","year":"2009","journal-title":"SIAM J. Numer. Anal."},{"key":"ref41","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TNN.2008.2005605","volume":"20","author":"Scarselli F.","year":"2009","journal-title":"IEEE Trans. Neural Networks"},{"key":"ref42","volume-title":"Stochastic Calculus for Finance : Continuous-Time Models","author":"Shreve S.","year":"2004"},{"key":"ref43","first-page":"1517","volume":"11","author":"Sriperumbudurm B.","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref44","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/17442509008833606","volume":"29","author":"Talay D.","year":"1990","journal-title":"Stochastics and Stochastic Reports"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1007\/s10444-018-9638-0","volume":"45","author":"Tang X.","year":"2019","journal-title":"Adv. Comput. Math."},{"key":"ref47","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1214\/aoap\/1015345301","volume":"11","author":"Wiktorsson M.","year":"2001","journal-title":"Ann. Appl. Probab."}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T09:00:45Z","timestamp":1759482045000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M161077X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,3]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12,31]]}},"alternative-id":["10.1137\/23M161077X"],"URL":"https:\/\/doi.org\/10.1137\/23m161077x","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,3]]}}}