{"id":"https://openalex.org/W4206250553","doi":"https://doi.org/10.1080/03610918.2021.2023181","title":"Viability for It\u00f4 stochastic systems with non-Lipschitzian coefficients and its application","display_name":"Viability for It\u00f4 stochastic systems with non-Lipschitzian coefficients and its application","publication_year":2022,"publication_date":"2022-01-03","ids":{"openalex":"https://openalex.org/W4206250553","doi":"https://doi.org/10.1080/03610918.2021.2023181"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2021.2023181","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.2023181","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"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":"Communications in Statistics - Simulation and Computation","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/A5014855921","display_name":"Xuejun Shi","orcid":"https://orcid.org/0000-0002-6276-5055"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuejun Shi","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079878207","display_name":"Qun Feng","orcid":"https://orcid.org/0000-0002-5329-4941"},"institutions":[{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qun Feng","raw_affiliation_strings":["Business School, University of Jinan, Jinan, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Business School, University of Jinan, Jinan, Shandong, China","institution_ids":["https://openalex.org/I34949971"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014855921"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01791216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"1","first_page":"446","last_page":"456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9986000061035156,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7567067742347717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6598930954933167},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6148889064788818},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5629910826683044},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.5627984404563904},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5486352443695068},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5187861919403076},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4565425217151642},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.42010697722435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3210994005203247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2539200782775879}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7567067742347717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6598930954933167},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6148889064788818},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5629910826683044},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.5627984404563904},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5486352443695068},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5187861919403076},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4565425217151642},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.42010697722435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3210994005203247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2539200782775879},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2021.2023181","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.2023181","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"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":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5716920026","display_name":null,"funder_award_id":"21CJY027","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G7666343415","display_name":null,"funder_award_id":"MG049,","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W579287291","https://openalex.org/W1602818694","https://openalex.org/W1779481391","https://openalex.org/W1969435656","https://openalex.org/W1971709781","https://openalex.org/W1984631587","https://openalex.org/W1997748558","https://openalex.org/W2051720297","https://openalex.org/W2054276304","https://openalex.org/W2061989553","https://openalex.org/W2077188730","https://openalex.org/W2097196681","https://openalex.org/W2102304678","https://openalex.org/W2300974746","https://openalex.org/W2577296667","https://openalex.org/W2594344391","https://openalex.org/W2761878242","https://openalex.org/W2790389815","https://openalex.org/W2891367590","https://openalex.org/W2920924004","https://openalex.org/W2945649898","https://openalex.org/W2963606286","https://openalex.org/W3131732985","https://openalex.org/W3156958163","https://openalex.org/W6737924044"],"related_works":["https://openalex.org/W620239920","https://openalex.org/W2549808526","https://openalex.org/W109055908","https://openalex.org/W2060658157","https://openalex.org/W2734530159","https://openalex.org/W1546584948","https://openalex.org/W2972896374","https://openalex.org/W2003428159","https://openalex.org/W2164842548","https://openalex.org/W2085400897"],"abstract_inverted_index":{"In":[0],"this":[1,46],"article,":[2],"we":[3,48],"study":[4],"the":[5,8,19,23,50],"viability":[6,33],"for":[7,32],"multi-dimensional":[9,51],"stochastic":[10,15,55],"system":[11],"described":[12],"by":[13],"It\u00f4":[14],"differential":[16,56],"equations":[17],"under":[18],"non-Lipschitzian":[20],"assumption":[21],"on":[22],"coefficients.":[24],"We":[25],"establish":[26],"a":[27,38],"necessary":[28],"and":[29],"sufficient":[30],"condition":[31],"property":[34],"with":[35,45],"respect":[36],"to":[37],"given":[39],"nonempty":[40],"closed":[41],"convex":[42],"set.":[43],"And":[44],"result,":[47],"explore":[49],"comparison":[52],"theorems":[53],"about":[54],"equations.":[57]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
