{"id":"https://openalex.org/W2522892054","doi":"https://doi.org/10.1137/16m1094117","title":"Spectral Methods for Multiscale Stochastic Differential Equations","display_name":"Spectral Methods for Multiscale Stochastic Differential Equations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2522892054","doi":"https://doi.org/10.1137/16m1094117","mag":"2522892054"},"language":"en","primary_location":{"id":"doi:10.1137/16m1094117","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1094117","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1094117","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1094117","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066396148","display_name":"Assyr Abdulle","orcid":"https://orcid.org/0000-0002-5687-9742"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Abdulle","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044857425","display_name":"Grigorios A. Pavliotis","orcid":"https://orcid.org/0000-0002-3468-9227"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. A. Pavliotis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029420841","display_name":"Urbain Vaes","orcid":"https://orcid.org/0000-0002-7629-7184"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"U. Vaes","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066396148"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":{"value":2777,"currency":"EUR","value_usd":2994},"fwci":1.6486,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8465945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"720","last_page":"761"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976999759674072,"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/spectral-method","display_name":"Spectral method","score":0.6819599270820618},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6490687131881714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6103336811065674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5548692941665649},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5192356705665588},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.470512330532074},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.45116639137268066},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.43533483147621155},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.42696407437324524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3851255476474762},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3715311288833618},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26604095101356506},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.18075621128082275}],"concepts":[{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.6819599270820618},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6490687131881714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6103336811065674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5548692941665649},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5192356705665588},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.470512330532074},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.45116639137268066},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.43533483147621155},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.42696407437324524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3851255476474762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3715311288833618},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26604095101356506},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.18075621128082275},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1094117","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1094117","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1094117","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.tind.io:221499","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/221499","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"research article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/44400","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/44400","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"761","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1137/16m1094117","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1094117","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1094117","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1045913000","display_name":null,"funder_award_id":"EP/L025159","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2354669367","display_name":null,"funder_award_id":"EP/L020564","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5348725440","display_name":null,"funder_award_id":"EP/L020564/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6731907685","display_name":null,"funder_award_id":"EP/L024926","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8552877082","display_name":null,"funder_award_id":"EP/L024926/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8730730436","display_name":null,"funder_award_id":"EP/L025159/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2522892054.pdf","grobid_xml":"https://content.openalex.org/works/W2522892054.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1482888786","https://openalex.org/W1521722756","https://openalex.org/W1572902284","https://openalex.org/W1646309082","https://openalex.org/W1965413319","https://openalex.org/W1978275259","https://openalex.org/W1979411153","https://openalex.org/W1984568974","https://openalex.org/W1987236926","https://openalex.org/W1998754480","https://openalex.org/W1999425740","https://openalex.org/W2012059548","https://openalex.org/W2020366183","https://openalex.org/W2027863489","https://openalex.org/W2039140382","https://openalex.org/W2065017332","https://openalex.org/W2070460788","https://openalex.org/W2078798756","https://openalex.org/W2078959912","https://openalex.org/W2089329494","https://openalex.org/W2090857812","https://openalex.org/W2094866248","https://openalex.org/W2098645609","https://openalex.org/W2117865287","https://openalex.org/W2118214292","https://openalex.org/W2138940269","https://openalex.org/W2139139723","https://openalex.org/W2141361312","https://openalex.org/W2157612169","https://openalex.org/W2243321271","https://openalex.org/W2341746487","https://openalex.org/W2401363764","https://openalex.org/W2963269142","https://openalex.org/W2964112122","https://openalex.org/W3105127227","https://openalex.org/W4213367101","https://openalex.org/W4238063566","https://openalex.org/W4245280614"],"related_works":["https://openalex.org/W4383100562","https://openalex.org/W175020571","https://openalex.org/W2952892835","https://openalex.org/W3105350940","https://openalex.org/W2053563337","https://openalex.org/W2125772108","https://openalex.org/W834379","https://openalex.org/W77325401","https://openalex.org/W2164734904","https://openalex.org/W3164382911"],"abstract_inverted_index":{"This":[0],"paper":[1,42],"presents":[2],"a":[3,45,53],"new":[4,46],"method":[5,28],"for":[6],"the":[7,15,25,31,67,81,84,97,101,104,109],"solution":[8,68],"of":[9,69,83,103],"multiscale":[10,27],"stochastic":[11,117],"differential":[12],"equations":[13],"at":[14],"diffusive":[16],"time":[17],"scale.":[18],"In":[19,56],"contrast":[20],"to":[21,65,79,114],"averaging-based":[22],"methods,":[23],"e.g.,":[24],"heterogeneous":[26],"(HMM)":[29],"or":[30],"equation-free":[32],"method,":[33],"which":[34,74],"rely":[35],"on":[36,52],"Monte":[37],"Carlo":[38],"simulations,":[39],"in":[40,62,77],"this":[41],"we":[43,58],"introduce":[44],"numerical":[47],"methodology":[48],"that":[49],"is":[50,75,89],"based":[51],"spectral":[54],"method.":[55,105],"particular,":[57],"use":[59],"an":[60,70,112],"expansion":[61],"Hermite":[63],"functions":[64],"approximate":[66],"appropriate":[71],"Poisson":[72],"equation,":[73],"used":[76],"order":[78],"calculate":[80],"coefficients":[82],"homogenized":[85],"equation.":[86],"Spectral":[87],"convergence":[88],"proved":[90],"under":[91],"suitable":[92],"assumptions.":[93],"Numerical":[94],"experiments":[95],"corroborate":[96],"theory":[98],"and":[99,111],"illustrate":[100],"performance":[102],"A":[106],"comparison":[107],"with":[108],"HMM":[110],"application":[113],"singularly":[115],"perturbed":[116],"PDEs":[118],"are":[119],"also":[120],"presented.":[121]},"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":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}
