{"id":"https://openalex.org/W7160513430","doi":"https://doi.org/10.48550/arxiv.2605.04480","title":"Geometric Milstein Scheme for Stochastic Differential Equations on SO(n) and SE(n)","display_name":"Geometric Milstein Scheme for Stochastic Differential Equations on SO(n) and SE(n)","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160513430","doi":"https://doi.org/10.48550/arxiv.2605.04480"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04480","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04480","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.04480","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135595847","display_name":"Xi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xi","raw_affiliation_strings":[],"raw_orcid":null,"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":"Solo, Victor","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.4893999993801117,"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":0.4893999993801117,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.15489999949932098,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.08799999952316284,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6628000140190125},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5985999703407288},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5867000222206116},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5770000219345093},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.4771000146865845},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4478999972343445},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4065000116825104},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.3894999921321869},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3529999852180481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8312000036239624},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6628000140190125},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5985999703407288},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5867000222206116},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5770000219345093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5472999811172485},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.4771000146865845},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4065000116825104},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3529999852180481},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.30570000410079956},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.2921999990940094},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.28769999742507935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.27480000257492065},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C25630934","wikidata":"https://www.wikidata.org/wiki/Q7379855","display_name":"Runge\u2013Kutta method","level":5,"score":0.2623000144958496},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.2583000063896179}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04480","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04480","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.04480","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04480","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"the":[1,17,33,38,59,69,81,103,121,126,131],"paper,":[2],"we":[3,49],"propose":[4],"a":[5,51,75],"higher-order":[6,41,98],"geometry-preserving":[7],"numerical":[8],"method":[9,56,77],"for":[10,78],"stochastic":[11,42,70,90],"differential":[12],"equations":[13],"(SDEs)":[14],"evolving":[15],"on":[16,29],"Lie":[18,25,79],"groups":[19],"SO(n)":[20],"and":[21,87,97,115,124,128],"SE(n).":[22],"Most":[23],"existing":[24],"group":[26],"integrators":[27],"rely":[28],"Magnus":[30],"expansion":[31],"of":[32,40,109,130],"exponential":[34],"map,":[35],"which":[36],"makes":[37],"construction":[39],"schemes":[43],"difficult.":[44],"To":[45],"overcome":[46],"this":[47],"limitation,":[48],"develop":[50],"tangent-space":[52],"parameterization":[53,62],"corrected":[54],"Milstein":[55],"(TaSP-CM),":[57],"extending":[58],"tangent":[60],"space":[61],"(TaSP)":[63],"framework":[64],"from":[65],"Lie-group":[66],"ODEs":[67],"to":[68,83],"setting.":[71],"Although":[72],"TaSP":[73],"is":[74,85],"well-established":[76],"ODEs,":[80],"extension":[82],"SDEs":[84],"non-trivial":[86],"requires":[88],"new":[89],"corrections":[91],"that":[92,102],"ensure":[93],"both":[94,113],"geometric":[95],"consistency":[96],"accuracy.":[99],"We":[100],"prove":[101],"proposed":[104,132],"scheme":[105],"achieves":[106],"strong":[107],"convergence":[108],"order":[110],"1":[111],"under":[112],"commutative":[114],"non-commutative":[116],"noise.":[117],"Numerical":[118],"experiments":[119],"illustrate":[120],"theoretical":[122],"results":[123],"demonstrate":[125],"efficiency":[127],"robustness":[129],"method.":[133]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-08T00:00:00"}
