{"id":"https://openalex.org/W3013078078","doi":"https://doi.org/10.1134/s0005117920030029","title":"On Weak Solutions of Highly Degenerate SDEs","display_name":"On Weak Solutions of Highly Degenerate SDEs","publication_year":2020,"publication_date":"2020-03-01","ids":{"openalex":"https://openalex.org/W3013078078","doi":"https://doi.org/10.1134/s0005117920030029","mag":"3013078078"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117920030029","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117920030029","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote 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/A5070425488","display_name":"A. Yu. Veretennikov","orcid":"https://orcid.org/0000-0001-8478-0515"},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]},{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB","RU"],"is_corresponding":true,"raw_author_name":"A. Yu. Veretennikov","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, Moscow, Russia","National Research University Higher School of Economics, Moscow, Russia","University of Leeds, Leeds, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"National Research University Higher School of Economics, Moscow, Russia","institution_ids":["https://openalex.org/I118501908"]},{"raw_affiliation_string":"University of Leeds, Leeds, United Kingdom","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070425488"],"corresponding_institution_ids":["https://openalex.org/I118501908","https://openalex.org/I130828816","https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":0.7113,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73706583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"81","issue":"3","first_page":"398","last_page":"410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9912999868392944,"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/T13234","display_name":"advanced mathematical theories","score":0.9829999804496765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/girsanov-theorem","display_name":"Girsanov theorem","score":0.9739329814910889},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.8762896060943604},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8528310060501099},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.7354847192764282},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6552786827087402},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6228463053703308},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5499255061149597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5408220291137695},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.493496298789978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36394554376602173},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3536248207092285},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17846623063087463},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0641721785068512}],"concepts":[{"id":"https://openalex.org/C104824951","wikidata":"https://www.wikidata.org/wiki/Q830124","display_name":"Girsanov theorem","level":3,"score":0.9739329814910889},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8762896060943604},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8528310060501099},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7354847192764282},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6552786827087402},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6228463053703308},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5499255061149597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5408220291137695},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.493496298789978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36394554376602173},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3536248207092285},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17846623063087463},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0641721785068512},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":2,"locations":[{"id":"doi:10.1134/s0005117920030029","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117920030029","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:161791","is_oa":false,"landing_page_url":"http://eprints.whiterose.ac.uk/161791/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"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":26,"referenced_works":["https://openalex.org/W45777778","https://openalex.org/W197246843","https://openalex.org/W1513091520","https://openalex.org/W1514451635","https://openalex.org/W1537833408","https://openalex.org/W1540113096","https://openalex.org/W1577527822","https://openalex.org/W1580561995","https://openalex.org/W1980073551","https://openalex.org/W2015500968","https://openalex.org/W2058250997","https://openalex.org/W2083731191","https://openalex.org/W2086633149","https://openalex.org/W2094649962","https://openalex.org/W2095012640","https://openalex.org/W2157560672","https://openalex.org/W2171307019","https://openalex.org/W2293139553","https://openalex.org/W2406624004","https://openalex.org/W2496454265","https://openalex.org/W2764299499","https://openalex.org/W2950768074","https://openalex.org/W2963878734","https://openalex.org/W3125617456","https://openalex.org/W4206788492","https://openalex.org/W4291213039"],"related_works":["https://openalex.org/W2024346620","https://openalex.org/W4302616869","https://openalex.org/W2949552611","https://openalex.org/W65301958","https://openalex.org/W4293505997","https://openalex.org/W3091465394","https://openalex.org/W2293312099","https://openalex.org/W2381203040","https://openalex.org/W3088883651","https://openalex.org/W3196785967"],"abstract_inverted_index":{"The":[0],"existence":[1],"and":[2],"weak":[3,7],"uniqueness":[4],"of":[5,9],"a":[6,10],"solution":[8],"highly":[11],"degenerate":[12],"stochastic":[13],"differential":[14],"equation,":[15],"along":[16],"with":[17],"its":[18],"local":[19],"mixing":[20],"property,":[21],"are":[22],"established":[23],"via":[24],"Girsanov\u2019s":[25],"transformation.":[26]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}