{"id":"https://openalex.org/W2045964026","doi":"https://doi.org/10.1137/040610507","title":"Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times","display_name":"Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2045964026","doi":"https://doi.org/10.1137/040610507","mag":"2045964026"},"language":"en","primary_location":{"id":"doi:10.1137/040610507","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040610507","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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/A5044857425","display_name":"Grigorios A. Pavliotis","orcid":"https://orcid.org/0000-0002-3468-9227"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G. A. Pavliotis","raw_affiliation_strings":["Mathematics Institute, Warwick University, Coventry CV4 7AL, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, Warwick University, Coventry CV4 7AL, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032114852","display_name":"Andrew M. Stuart","orcid":"https://orcid.org/0000-0001-9091-7266"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. M. Stuart","raw_affiliation_strings":["Mathematics Institute, Warwick University, Coventry CV4 7AL, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, Warwick University, Coventry CV4 7AL, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":1.1709,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.74156422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"1","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9987999796867371,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.7582694292068481},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6550419330596924},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.6237215995788574},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.6070472598075867},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5600752234458923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5500258207321167},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5448950529098511},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.49436473846435547},{"id":"https://openalex.org/keywords/colors-of-noise","display_name":"Colors of noise","score":0.46788209676742554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4640212655067444},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.44621190428733826},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4410381317138672},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3109646737575531},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08015349507331848},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07655209302902222},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.076302170753479}],"concepts":[{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.7582694292068481},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6550419330596924},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6237215995788574},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.6070472598075867},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5600752234458923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5500258207321167},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5448950529098511},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49436473846435547},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.46788209676742554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4640212655067444},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.44621190428733826},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4410381317138672},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3109646737575531},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08015349507331848},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07655209302902222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.076302170753479},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040610507","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040610507","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.340.4390","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.340.4390","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math-ph/0504054v1.pdf","raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:78109","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170612-130002475","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"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":35,"referenced_works":["https://openalex.org/W37835502","https://openalex.org/W154031314","https://openalex.org/W1481161909","https://openalex.org/W1562147356","https://openalex.org/W1906036866","https://openalex.org/W1970811411","https://openalex.org/W1978326559","https://openalex.org/W1983097489","https://openalex.org/W1986101505","https://openalex.org/W1992111513","https://openalex.org/W1995171785","https://openalex.org/W2002484346","https://openalex.org/W2009348158","https://openalex.org/W2020032873","https://openalex.org/W2028771344","https://openalex.org/W2051877345","https://openalex.org/W2052288546","https://openalex.org/W2082389346","https://openalex.org/W2083663860","https://openalex.org/W2084531879","https://openalex.org/W2089290407","https://openalex.org/W2090693357","https://openalex.org/W2092818343","https://openalex.org/W2096223869","https://openalex.org/W2127673851","https://openalex.org/W2139798591","https://openalex.org/W2152696833","https://openalex.org/W2158374803","https://openalex.org/W2799664482","https://openalex.org/W4206537305","https://openalex.org/W4206558387","https://openalex.org/W4210519891","https://openalex.org/W4213329537","https://openalex.org/W4300023393","https://openalex.org/W4300475775"],"related_works":["https://openalex.org/W2349980442","https://openalex.org/W2790395016","https://openalex.org/W3143465902","https://openalex.org/W2607263052","https://openalex.org/W2568148104","https://openalex.org/W2071543241","https://openalex.org/W2112901162","https://openalex.org/W2147481109","https://openalex.org/W1973144160","https://openalex.org/W2922917287"],"abstract_inverted_index":{"In":[0,98],"this":[1,22,167],"paper":[2,23],"we":[3,66,100],"present":[4],"a":[5,26,120],"rigorous":[6],"asymptotic":[7],"analysis":[8],"for":[9,29,181],"stochastic":[10],"systems":[11],"with":[12,33],"two":[13,91,108],"fast":[14,92],"relaxation":[15,51,109],"times.":[16],"The":[17],"mathematical":[18],"model":[19],"analyzed":[20],"in":[21,103,123],"consists":[24],"of":[25,59,89,95,133,149,184],"Langevin":[27],"equation":[28,83],"the":[30,46,49,56,60,68,75,81,86,90,96,104,107,115,126,138,141,147,153,157,162,182,185],"particle":[31,50,150],"motion":[32],"time-dependent":[34],"force":[35],"constructed":[36],"through":[37],"an":[38],"infinite":[39],"dimensional":[40],"Gaussian":[41,76],"noise":[42,61,143,163],"process.":[43],"We":[44,78],"study":[45],"limit":[47],"as":[48,53,55],"time":[52,58,93],"well":[54],"correlation":[57],"tend":[62],"to":[63,112,125],"zero,":[64],"and":[65],"obtain":[67],"limiting":[69,82,127],"equations":[70],"under":[71],"appropriate":[72],"assumptions":[73],"on":[74,85,137,146,166],"noise.":[77],"show":[79],"that":[80,102],"depends":[84],"relative":[87],"magnitude":[88],"scales":[94],"system.":[97],"particular,":[99],"prove":[101],"case":[105],"where":[106],"times":[110],"converge":[111],"zero":[113],"at":[114],"same":[116],"rate":[117],"there":[118,170],"is":[119,131,144,156,164,171],"drift":[121,154,173],"correction,":[122],"addition":[124],"It\u00f4":[128],"integral,":[129],"which":[130],"not":[132],"Stratonovich":[134,159],"type.":[135],"If,":[136],"other":[139],"hand,":[140],"colored":[142],"smooth":[145],"scale":[148],"relaxation,":[151],"then":[152,169],"correction":[155],"standard":[158],"correction.":[160,174],"If":[161],"rough":[165],"scale,":[168],"no":[172],"Strong":[175],"(i.e.,":[176],"pathwise)":[177],"techniques":[178],"are":[179],"used":[180],"proof":[183],"convergence":[186],"theorems.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
