{"id":"https://openalex.org/W2025245059","doi":"https://doi.org/10.1137/040614426","title":"Numerical Algorithms for Forward-Backward Stochastic Differential Equations","display_name":"Numerical Algorithms for Forward-Backward Stochastic Differential Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2025245059","doi":"https://doi.org/10.1137/040614426","mag":"2025245059"},"language":"en","primary_location":{"id":"doi:10.1137/040614426","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614426","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066964804","display_name":"Grigori N. Milstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. N. Milstein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081243775","display_name":"M. V. Tretyakov","orcid":"https://orcid.org/0000-0002-7929-9046"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. V. Tretyakov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5002,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.92788707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"28","issue":"2","first_page":"561","last_page":"582"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9057930707931519},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5860407948493958},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5845030546188354},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5426715612411499},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47998329997062683},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43787044286727905},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4329512417316437},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4323872923851013},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43054690957069397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39906951785087585}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9057930707931519},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5860407948493958},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5845030546188354},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5426715612411499},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47998329997062683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43787044286727905},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4329512417316437},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4323872923851013},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43054690957069397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39906951785087585},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040614426","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614426","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:lra.le.ac.uk:2381/2425","is_oa":false,"landing_page_url":"http://hdl.handle.net/2381/2425","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W38661520","https://openalex.org/W84156084","https://openalex.org/W94839203","https://openalex.org/W584445507","https://openalex.org/W659339155","https://openalex.org/W1525883337","https://openalex.org/W1587029759","https://openalex.org/W1966177997","https://openalex.org/W1994791309","https://openalex.org/W1998499117","https://openalex.org/W2041802328","https://openalex.org/W2046553535","https://openalex.org/W2050624780","https://openalex.org/W2052849518","https://openalex.org/W2052883417","https://openalex.org/W2066221740","https://openalex.org/W2081458347","https://openalex.org/W2085672697","https://openalex.org/W2090857110","https://openalex.org/W2138297771","https://openalex.org/W2157883119","https://openalex.org/W2160964994","https://openalex.org/W2369386221","https://openalex.org/W2480404596","https://openalex.org/W4212780424","https://openalex.org/W4240361988","https://openalex.org/W4300143132"],"related_works":["https://openalex.org/W1967450583","https://openalex.org/W2066764747","https://openalex.org/W2385175414","https://openalex.org/W2083817219","https://openalex.org/W2264582182","https://openalex.org/W4389325770","https://openalex.org/W3047860677","https://openalex.org/W2969693569","https://openalex.org/W2343093002","https://openalex.org/W3131706438"],"abstract_inverted_index":{"Efficient":[0],"numerical":[1,130],"algorithms":[2,39,105,117],"are":[3,40,61,79,100,127],"proposed":[4],"for":[5,47,106,118],"a":[6,66,109],"class":[7],"of":[8,65,71,75,92],"forward-backward":[9],"stochastic":[10],"differential":[11,19],"equations":[12],"(FBSDEs)":[13],"connected":[14],"with":[15,103,120],"semilinear":[16,52,77],"parabolic":[17,53],"partial":[18],"equations.":[20],"As":[21],"in":[22],"[J.":[23],"Douglas,":[24],"Jr.,":[25],"J.":[26],"Ma,":[27],"and":[28,95],"P.":[29],"Protter,":[30],"Ann.":[31],"Appl.":[32],"Probab.,":[33],"6":[34],"(1996),":[35],"pp.":[36],"940-968],":[37],"the":[38,43,72,76,104],"based":[41],"on":[42,108],"known":[44],"four-step":[45],"scheme":[46],"solving":[48],"FBSDEs.":[49],"The":[50,69,84,124],"corresponding":[51],"equation":[54,78,86],"is":[55,87],"solved":[56],"by":[57,63,81,89,129],"layer":[58],"methods":[59,91],"which":[60],"constructed":[62],"means":[64],"probabilistic":[67],"approach.":[68],"derivatives":[70],"solution":[73],"u":[74],"found":[80],"finite":[82,111],"differences.":[83],"forward":[85],"simulated":[88],"mean-square":[90],"order":[93],"1/2":[94],"1.":[96],"Corresponding":[97],"convergence":[98],"theorems":[99],"proved.":[101],"Along":[102],"FBSDEs":[107,119],"fixed":[110],"time":[112],"interval,":[113],"we":[114],"also":[115],"construct":[116],"random":[121],"terminal":[122],"time.":[123],"results":[125],"obtained":[126],"supported":[128],"experiments.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}