{"id":"https://openalex.org/W2515882314","doi":"https://doi.org/10.1137/15m1019726","title":"Geometric Euler--Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n)","display_name":"Geometric Euler--Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n)","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2515882314","doi":"https://doi.org/10.1137/15m1019726","mag":"2515882314"},"language":"en","primary_location":{"id":"doi:10.1137/15m1019726","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019726","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://handle.unsw.edu.au/1959.4/unsworks_41877","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056263605","display_name":"Marc J. Piggott","orcid":"https://orcid.org/0000-0001-5576-8867"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. J. Piggott","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091154507","display_name":"Victor Solo","orcid":"https://orcid.org/0000-0002-5123-7708"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Solo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056263605"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3453,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89544485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"4","first_page":"2490","last_page":"2516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9966999888420105,"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":0.9966999888420105,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8518736362457275},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6446848511695862},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6213396787643433},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5859273672103882},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5733271241188049},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5370781421661377},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5219259262084961},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43062546849250793},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.41524776816368103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3151087164878845},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17235666513442993}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8518736362457275},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6446848511695862},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6213396787643433},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5859273672103882},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5733271241188049},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5370781421661377},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5219259262084961},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43062546849250793},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.41524776816368103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3151087164878845},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17235666513442993},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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":3,"locations":[{"id":"doi:10.1137/15m1019726","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019726","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:unsworks.unsw.edu.au:1959.4/unsworks_41877","is_oa":true,"landing_page_url":"http://handle.unsw.edu.au/1959.4/unsworks_41877","pdf_url":null,"source":{"id":"https://openalex.org/S4377196481","display_name":"UNSWorks (UNSW Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31746571","host_organization_name":"UNSW Sydney","host_organization_lineage":["https://openalex.org/I31746571"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:unsworks.library.unsw.edu.au:1959.4/unsworks_41877","is_oa":true,"landing_page_url":"http://hdl.handle.net/1959.4/unsworks_41877","pdf_url":null,"source":{"id":"https://openalex.org/S4306401737","display_name":"UNSWorks (University of New South Wales, Sydney, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40053085","host_organization_name":"Australian Defence Force Academy","host_organization_lineage":["https://openalex.org/I40053085"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 54, 4, 2490-2516","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"pmh:oai:unsworks.unsw.edu.au:1959.4/unsworks_41877","is_oa":true,"landing_page_url":"http://handle.unsw.edu.au/1959.4/unsworks_41877","pdf_url":null,"source":{"id":"https://openalex.org/S4377196481","display_name":"UNSWorks (UNSW Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31746571","host_organization_name":"UNSW Sydney","host_organization_lineage":["https://openalex.org/I31746571"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4474778494","display_name":null,"funder_award_id":"DP140102041","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1583323312","https://openalex.org/W1651042827","https://openalex.org/W1970935533","https://openalex.org/W1978275259","https://openalex.org/W1979674792","https://openalex.org/W1981041413","https://openalex.org/W1987903845","https://openalex.org/W1990647940","https://openalex.org/W1992278142","https://openalex.org/W1994384777","https://openalex.org/W2015187789","https://openalex.org/W2016012557","https://openalex.org/W2021311647","https://openalex.org/W2031958704","https://openalex.org/W2032090338","https://openalex.org/W2039185476","https://openalex.org/W2049046732","https://openalex.org/W2050660811","https://openalex.org/W2067765618","https://openalex.org/W2076365222","https://openalex.org/W2080930962","https://openalex.org/W2082618321","https://openalex.org/W2083763944","https://openalex.org/W2084564496","https://openalex.org/W2084902777","https://openalex.org/W2090455737","https://openalex.org/W2092752743","https://openalex.org/W2094210680","https://openalex.org/W2106565812","https://openalex.org/W2116228907","https://openalex.org/W2118323590","https://openalex.org/W2119968067","https://openalex.org/W2120516507","https://openalex.org/W2131838761","https://openalex.org/W2133632163","https://openalex.org/W2140393629","https://openalex.org/W2141020323","https://openalex.org/W2144707556","https://openalex.org/W2151249889","https://openalex.org/W2154062528","https://openalex.org/W2158020678","https://openalex.org/W2160619958","https://openalex.org/W2162122651","https://openalex.org/W2324349653","https://openalex.org/W2913502585","https://openalex.org/W3105647143"],"related_works":["https://openalex.org/W2135584473","https://openalex.org/W2964223869","https://openalex.org/W2626141450","https://openalex.org/W2114045837","https://openalex.org/W2792539140","https://openalex.org/W2005808740","https://openalex.org/W2295130398","https://openalex.org/W4302055909","https://openalex.org/W4312805195","https://openalex.org/W2111177161"],"abstract_inverted_index":{"We":[0],"consider":[1],"numerical":[2],"schemes":[3,14,32],"for":[4,27],"simulating":[5],"diffusions":[6],"that":[7,42],"evolve":[8],"in":[9,47,65],"SO(n)":[10],"and":[11,24],"SE(n).":[12],"Surprisingly,":[13],"based":[15,33],"on":[16,34],"the":[17,28,43,48,58],"exponential":[18],"Rodrigues":[19],"formula":[20],"have":[21],"conditioning":[22],"problems,":[23],"we":[25,52],"develop":[26,53],"first":[29,59,62],"time":[30],"reliable":[31],"diagonal":[35],"Pad\u00e9":[36],"approximants.":[37],"A":[38],"crucial":[39],"feature":[40],"is":[41],"simulated":[44],"trajectories":[45],"lie":[46],"respective":[49],"manifolds.":[50],"Also":[51],"what":[54],"appear":[55],"to":[56],"be":[57],"results":[60],"guaranteeing":[61],"order":[63],"convergence":[64],"mean":[66],"uniform":[67],"squared":[68],"error.":[69],"The":[70],"algorithms":[71],"are":[72],"illustrated":[73],"with":[74],"simulations.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}