{"id":"https://openalex.org/W3010881130","doi":"https://doi.org/10.1080/00207179.2020.1740794","title":"Quasi-sure exponential stability and stabilisation of stochastic delay differential equations under <i>G</i>-expectation framework","display_name":"Quasi-sure exponential stability and stabilisation of stochastic delay differential equations under <i>G</i>-expectation framework","publication_year":2020,"publication_date":"2020-03-11","ids":{"openalex":"https://openalex.org/W3010881130","doi":"https://doi.org/10.1080/00207179.2020.1740794","mag":"3010881130"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2020.1740794","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2020.1740794","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5069207511","display_name":"Wensheng Yin","orcid":"https://orcid.org/0000-0001-7634-7607"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wensheng Yin","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, People's Republic of China","School of Mathematics, Southeast University, Nanjing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017004747","display_name":"Yong Ren","orcid":"https://orcid.org/0000-0002-8353-6788"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Ren","raw_affiliation_strings":["School of Mathematics & Statistics, Anhui Normal University, Wuhu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics & Statistics, Anhui Normal University, Wuhu, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017808266"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":1.1694,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80452854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"94","issue":"10","first_page":"2874","last_page":"2885"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9987999796867371,"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"}},"topics":[{"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11720","display_name":"Probability and Risk Models","score":0.9623000025749207,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/exponential-stability","display_name":"Exponential stability","score":0.750339686870575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7502076625823975},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6058327555656433},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5824780464172363},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5577064752578735},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5255730748176575},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5141318440437317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47065654397010803},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.45978879928588867},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4579440951347351},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39377880096435547},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30242931842803955},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16070520877838135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11890295147895813},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09328150749206543},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08186715841293335},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06749570369720459}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.750339686870575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7502076625823975},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6058327555656433},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5824780464172363},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5577064752578735},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5255730748176575},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5141318440437317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47065654397010803},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.45978879928588867},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4579440951347351},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39377880096435547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30242931842803955},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16070520877838135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11890295147895813},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09328150749206543},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08186715841293335},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06749570369720459},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2020.1740794","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2020.1740794","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4585534567","display_name":"\u57fa\u4e8e\u7fa4\u4f53\u667a\u80fd\u7684\u5206\u5e03\u5f0f\u4f18\u5316\u7406\u8bba\u3001\u65b9\u6cd5\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"61833005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6943839511","display_name":"\u7531G-\u5e03\u6717\u8fd0\u52a8\u9a71\u52a8\u7684\u51e0\u7c7b\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u7814\u7a76","funder_award_id":"11871076","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1494628843","https://openalex.org/W1505057802","https://openalex.org/W1564920178","https://openalex.org/W1639879014","https://openalex.org/W1992382156","https://openalex.org/W2006145256","https://openalex.org/W2016116013","https://openalex.org/W2018860013","https://openalex.org/W2048677413","https://openalex.org/W2054585000","https://openalex.org/W2072758217","https://openalex.org/W2079891793","https://openalex.org/W2097216668","https://openalex.org/W2129969123","https://openalex.org/W2154652229","https://openalex.org/W2160533459","https://openalex.org/W2288218753","https://openalex.org/W2291247895","https://openalex.org/W2321273752","https://openalex.org/W2411501272","https://openalex.org/W2474875956","https://openalex.org/W2556017170","https://openalex.org/W2735441869","https://openalex.org/W2742818715","https://openalex.org/W2745153931","https://openalex.org/W2766861893","https://openalex.org/W2767729146","https://openalex.org/W2790443650","https://openalex.org/W2807689777","https://openalex.org/W2855253609","https://openalex.org/W2889478524","https://openalex.org/W2902469690","https://openalex.org/W2912078486","https://openalex.org/W2952743423","https://openalex.org/W2964132972","https://openalex.org/W3122314732","https://openalex.org/W4235816940","https://openalex.org/W4241544126"],"related_works":["https://openalex.org/W126238052","https://openalex.org/W1593898832","https://openalex.org/W2142048021","https://openalex.org/W2756324413","https://openalex.org/W2383529437","https://openalex.org/W2134075948","https://openalex.org/W2119732617","https://openalex.org/W2952903495","https://openalex.org/W4299335823","https://openalex.org/W2954344910"],"abstract_inverted_index":{"In":[0],"this":[1,77],"work,":[2],"we":[3,35],"obtain":[4],"the":[5,40,43,50,61,71,82,94],"sufficient":[6],"conditions":[7],"to":[8,42,80,92],"examine":[9],"quasi-sure":[10,29,101],"exponential":[11,30,102],"stability":[12,31],"of":[13,32,45,100],"stochastic":[14],"delay":[15,73,83],"differential":[16],"equation":[17],"under":[18],"G-expectation":[19],"framework":[20],"(in":[21],"short,":[22],"G-SDDE).":[23],"Our":[24],"argument":[25],"is":[26,63],"based":[27],"on":[28],"G-SDE":[33],"and":[34],"should":[36],"point":[37],"out":[38],"that":[39,52,60],"keys":[41],"proof":[44],"our":[46],"main":[47],"result":[48],"are":[49],"fact":[51],"there":[53],"exists":[54],"a":[55],"positive":[56],"number":[57],"\u03c4\u2217":[58],"such":[59],"G-SDDE":[62],"also":[64],"quasi-surely":[65],"exponentially":[66],"stable":[67],"as":[68,70,91],"long":[69],"time":[72],"constant":[74],"\u03c4<\u03c4\u2217.":[75],"Furthermore,":[76],"approach":[78],"allows":[79],"design":[81],"feedback":[84],"control":[85],"induced":[86],"by":[87],"G-Brownian":[88],"motion":[89],"so":[90],"stabilise":[93],"given":[95],"deterministic":[96],"systems":[97],"in":[98],"terms":[99],"stability.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}