{"id":"https://openalex.org/W2612271500","doi":"https://doi.org/10.1137/17m113160x","title":"Type II Singular Perturbation Approximation for Linear Systems with L\u00e9vy Noise","display_name":"Type II Singular Perturbation Approximation for Linear Systems with L\u00e9vy Noise","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2612271500","doi":"https://doi.org/10.1137/17m113160x","mag":"2612271500"},"language":"en","primary_location":{"id":"doi:10.1137/17m113160x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m113160x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.20347/wias.preprint.2398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053852920","display_name":"Martin Redmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Redmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5053852920"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1844,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56419325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"56","issue":"3","first_page":"2120","last_page":"2158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.974399983882904,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.974399983882904,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4745132327079773},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4698335826396942},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36145657300949097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2699384093284607}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4745132327079773},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4698335826396942},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36145657300949097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2699384093284607},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m113160x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m113160x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:doi:10.20347/wias.preprint.2398","is_oa":false,"landing_page_url":"https://archive.wias-berlin.de/receive/test_mods_00000044?XSL.Transformer=mods","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"doi:10.20347/wias.preprint.2398","is_oa":true,"landing_page_url":"https://doi.org/10.20347/wias.preprint.2398","pdf_url":null,"source":{"id":"https://openalex.org/S7407053009","display_name":"Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.34657/3424","is_oa":true,"landing_page_url":"https://doi.org/10.34657/3424","pdf_url":null,"source":{"id":"https://openalex.org/S7407052981","display_name":"TIB Repositorium","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Report"},{"id":"mag:2612271500","is_oa":false,"landing_page_url":"http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2017&number=2398","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.20347/wias.preprint.2398","is_oa":true,"landing_page_url":"https://doi.org/10.20347/wias.preprint.2398","pdf_url":null,"source":{"id":"https://openalex.org/S7407053009","display_name":"Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[{"display_name":"Climate action","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1584666263","https://openalex.org/W1842378573","https://openalex.org/W1970636555","https://openalex.org/W1971634471","https://openalex.org/W2002858896","https://openalex.org/W2018164853","https://openalex.org/W2047312539","https://openalex.org/W2048550169","https://openalex.org/W2064733273","https://openalex.org/W2076621197","https://openalex.org/W2080493630","https://openalex.org/W2091015478","https://openalex.org/W2091160474","https://openalex.org/W2098364017","https://openalex.org/W2116813424","https://openalex.org/W2172066780","https://openalex.org/W2614367992","https://openalex.org/W4247755366","https://openalex.org/W4253629962"],"related_works":["https://openalex.org/W2808648567","https://openalex.org/W2743905828","https://openalex.org/W2963461292","https://openalex.org/W2895559316","https://openalex.org/W1975356123","https://openalex.org/W2494999475","https://openalex.org/W2963867670","https://openalex.org/W2351682845","https://openalex.org/W90981613","https://openalex.org/W2062736751","https://openalex.org/W2052162576","https://openalex.org/W2248503246","https://openalex.org/W136812962","https://openalex.org/W3104162674","https://openalex.org/W3099411898","https://openalex.org/W2009668663","https://openalex.org/W2019678069","https://openalex.org/W2545890133","https://openalex.org/W2091160474","https://openalex.org/W3143042683"],"abstract_inverted_index":{"When":[0],"solving":[1],"linear":[2,85],"stochastic":[3,73,126],"partial":[4],"differential":[5],"equations":[6],"numerically,":[7],"usually":[8],"a":[9,43,53],"high":[10],"order":[11,17,27,45],"spatial":[12],"discretization":[13],"is":[14,48,91],"needed.":[15],"Model":[16],"reduction":[18],"(MOR)":[19],"techniques":[20],"are":[21],"often":[22],"used":[23],"to":[24,41,72,84,155],"reduce":[25,34],"the":[26,81,100,130,137],"of":[28,80,112,132],"spatially":[29],"discretized":[30],"systems":[31,86],"and":[32,143],"hence":[33],"computational":[35],"complexity.":[36],"A":[37],"particular":[38],"MOR":[39],"technique":[40],"obtain":[42],"reduced":[44],"model":[46],"(ROM)":[47],"singular":[49],"perturbation":[50],"approximation":[51],"(SPA),":[52],"method":[54],"which":[55,90],"has":[56,68,107],"been":[57,70],"extensively":[58],"studied":[59],"for":[60,125,149],"deterministic":[61,82],"systems.":[62,158],"As":[63],"so-called":[64],"type":[65,93,104,114,140,150],"I":[66,115],"SPA":[67,106,152],"already":[69],"extended":[71],"equations.":[74],"We":[75],"provide":[76,121],"an":[77],"alternative":[78],"generalization":[79],"setting":[83],"with":[87],"L\u00e9vy":[88,156],"noise":[89],"called":[92],"II":[94,105,141,151],"SPA.":[95,116],"It":[96],"turns":[97],"out":[98],"that":[99,111],"ROM":[101,138],"from":[102],"applying":[103],"better":[108],"properties":[109],"than":[110],"using":[113],"In":[117],"this":[118],"paper,":[119],"we":[120],"new":[122],"energy":[123],"interpretations":[124],"reachability":[127],"Gramians,":[128],"show":[129],"preservation":[131],"mean":[133],"square":[134],"stability":[135],"in":[136],"by":[139],"SPA,":[142],"prove":[144],"two":[145],"different":[146],"error":[147],"bounds":[148],"when":[153],"applied":[154],"driven":[157]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}