{"id":"https://openalex.org/W4403538915","doi":"https://doi.org/10.3390/sym16101372","title":"Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein\u2013Uhlenbeck Process with Application to U.S. Treasury Rate Analysis","display_name":"Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein\u2013Uhlenbeck Process with Application to U.S. Treasury Rate Analysis","publication_year":2024,"publication_date":"2024-10-15","ids":{"openalex":"https://openalex.org/W4403538915","doi":"https://doi.org/10.3390/sym16101372"},"language":"en","primary_location":{"id":"doi:10.3390/sym16101372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101372","pdf_url":"https://www.mdpi.com/2073-8994/16/10/1372/pdf?version=1728995007","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/10/1372/pdf?version=1728995007","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005642041","display_name":"Anshui Li","orcid":"https://orcid.org/0000-0001-8259-9990"},"institutions":[{"id":"https://openalex.org/I192209268","display_name":"Shaoxing University","ror":"https://ror.org/0435tej63","country_code":"CN","type":"education","lineage":["https://openalex.org/I192209268"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anshui Li","raw_affiliation_strings":["School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"],"raw_orcid":"https://orcid.org/0000-0001-8259-9990","affiliations":[{"raw_affiliation_string":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China","institution_ids":["https://openalex.org/I192209268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100394323","display_name":"Jiajia Wang","orcid":"https://orcid.org/0000-0002-7028-9554"},"institutions":[{"id":"https://openalex.org/I192209268","display_name":"Shaoxing University","ror":"https://ror.org/0435tej63","country_code":"CN","type":"education","lineage":["https://openalex.org/I192209268"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiajia Wang","raw_affiliation_strings":["School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China","institution_ids":["https://openalex.org/I192209268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016839576","display_name":"Lianlian Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I192209268","display_name":"Shaoxing University","ror":"https://ror.org/0435tej63","country_code":"CN","type":"education","lineage":["https://openalex.org/I192209268"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lianlian Zhou","raw_affiliation_strings":["School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Physics and Information, Shaoxing University, Shaoxing 312000, China","institution_ids":["https://openalex.org/I192209268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016839576"],"corresponding_institution_ids":["https://openalex.org/I192209268"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.0326,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.87676219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"16","issue":"10","first_page":"1372","last_page":"1372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9901000261306763,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9805999994277954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ornstein\u2013uhlenbeck-process","display_name":"Ornstein\u2013Uhlenbeck process","score":0.853431224822998},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7321718335151672},{"id":"https://openalex.org/keywords/treasury","display_name":"Treasury","score":0.5731929540634155},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.5368464589118958},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5299526453018188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5218628644943237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4967535138130188},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.49357736110687256},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4890352189540863},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4366393983364105},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.41907763481140137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4182838201522827},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.41304242610931396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14639168977737427},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14050036668777466},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.13857501745224},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13321611285209656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08293235301971436}],"concepts":[{"id":"https://openalex.org/C31634936","wikidata":"https://www.wikidata.org/wiki/Q1757587","display_name":"Ornstein\u2013Uhlenbeck process","level":3,"score":0.853431224822998},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7321718335151672},{"id":"https://openalex.org/C2780889827","wikidata":"https://www.wikidata.org/wiki/Q10756188","display_name":"Treasury","level":2,"score":0.5731929540634155},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5368464589118958},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5299526453018188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5218628644943237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4967535138130188},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.49357736110687256},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4890352189540863},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4366393983364105},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.41907763481140137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4182838201522827},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.41304242610931396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14639168977737427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14050036668777466},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.13857501745224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13321611285209656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08293235301971436},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16101372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101372","pdf_url":"https://www.mdpi.com/2073-8994/16/10/1372/pdf?version=1728995007","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d3300ebfd826437487b4283f9be9b1e7","is_oa":false,"landing_page_url":"https://doaj.org/article/d3300ebfd826437487b4283f9be9b1e7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Symmetry, Vol 16, Iss 10, p 1372 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16101372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16101372","pdf_url":"https://www.mdpi.com/2073-8994/16/10/1372/pdf?version=1728995007","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G4782386762","display_name":null,"funder_award_id":"11901145","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403538915.pdf","grobid_xml":"https://content.openalex.org/works/W4403538915.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W632189368","https://openalex.org/W1511895114","https://openalex.org/W1606449868","https://openalex.org/W1815010800","https://openalex.org/W1984629873","https://openalex.org/W2021171753","https://openalex.org/W2042775870","https://openalex.org/W2045212949","https://openalex.org/W2127740852","https://openalex.org/W2132744305","https://openalex.org/W2139905755","https://openalex.org/W2142004657","https://openalex.org/W2151376743","https://openalex.org/W2164919501","https://openalex.org/W2168483283","https://openalex.org/W2190310860","https://openalex.org/W2230870193","https://openalex.org/W2515877265","https://openalex.org/W2953588946","https://openalex.org/W2971516139","https://openalex.org/W2972346427","https://openalex.org/W3037727996","https://openalex.org/W3093697920","https://openalex.org/W3141032587","https://openalex.org/W4210507064","https://openalex.org/W4220822722","https://openalex.org/W4245879216","https://openalex.org/W4248548705","https://openalex.org/W4281775731","https://openalex.org/W4293708200","https://openalex.org/W4327966584","https://openalex.org/W4387695665","https://openalex.org/W4390775587","https://openalex.org/W4399753183","https://openalex.org/W4400581142","https://openalex.org/W4400591873","https://openalex.org/W6630758492","https://openalex.org/W6638379661","https://openalex.org/W6678868654","https://openalex.org/W6682597882","https://openalex.org/W6687396190","https://openalex.org/W6689579949","https://openalex.org/W6784409675","https://openalex.org/W6792032619"],"related_works":["https://openalex.org/W1589100136","https://openalex.org/W2890373187","https://openalex.org/W1608748508","https://openalex.org/W4205411904","https://openalex.org/W3090783472","https://openalex.org/W4391959027","https://openalex.org/W171914860","https://openalex.org/W1969906963","https://openalex.org/W2060317829","https://openalex.org/W4249297485"],"abstract_inverted_index":{"Uncertain":[0],"differential":[1,8,30],"equations,":[2,9],"as":[3],"an":[4],"alternative":[5],"to":[6,12,115,125],"stochastic":[7],"have":[10],"proved":[11],"be":[13,141],"extremely":[14],"powerful":[15],"across":[16],"various":[17],"fields,":[18],"especially":[19,45],"in":[20,36,70,85,105,150],"finance":[21],"theory.":[22,87],"The":[23,153],"issue":[24],"of":[25,65,81,130],"parameter":[26,92],"estimation":[27,93],"for":[28],"uncertain":[29,55,74,145],"equations":[31],"is":[32,42],"the":[33,47,62,66,73,79,82,91,123,127,131,144],"key":[34],"step":[35],"mathematical":[37],"modeling":[38],"and":[39,159],"simulation,":[40],"which":[41,139],"very":[43],"difficult,":[44],"when":[46],"corresponding":[48,83],"terms":[49],"are":[50,103,113],"driven":[51],"by":[52,143],"some":[53],"complicated":[54],"processes.":[56],"In":[57],"this":[58,151],"paper,":[59],"we":[60],"propose":[61],"uncertainty":[63,86],"counterpart":[64],"threshold":[67,75,146],"Ornstein\u2013Uhlenbeck":[68,76,147],"process":[69,148],"probability,":[71],"named":[72],"process,":[77],"filling":[78],"gaps":[80],"research":[84],"We":[88,120],"then":[89],"explore":[90],"problem":[94],"under":[95],"different":[96],"scenarios,":[97],"including":[98],"cases":[99],"where":[100],"certain":[101],"parameters":[102],"known":[104],"advance":[106],"while":[107],"others":[108],"remain":[109],"unknown.":[110],"Numerical":[111],"examples":[112],"provided":[114],"illustrate":[116],"our":[117],"method":[118,124],"proposed.":[119],"also":[121],"apply":[122],"study":[126],"term":[128],"structure":[129],"U.S.":[132],"Treasury":[133],"rates":[134],"over":[135],"a":[136],"specific":[137],"period,":[138],"can":[140],"modeled":[142],"mentioned":[149],"paper.":[152],"paper":[154],"concludes":[155],"with":[156],"brief":[157],"remarks":[158],"possible":[160],"future":[161],"directions.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2024-10-19T00:00:00"}
