{"id":"https://openalex.org/W7207746411","doi":"https://doi.org/10.48550/arxiv.2609.02022","title":"Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts","display_name":"Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207746411","doi":"https://doi.org/10.48550/arxiv.2609.02022"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02022","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02022","pdf_url":"https://arxiv.org/pdf/2609.02022","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.02022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044550200","display_name":"Z. Q. Chen","orcid":"https://orcid.org/0000-0003-3155-8288","observed_orcids":["https://orcid.org/0000-0003-3155-8288"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Zikai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123422328","display_name":"Zimo Hao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao, Zimo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5149923418","display_name":"Xicheng Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xicheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.5776000022888184,"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":0.5776000022888184,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.15299999713897705,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.07180000096559525,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.9160000085830688},{"id":"https://openalex.org/keywords/distribution-shift","display_name":"distribution shift","score":0.7429999709129333},{"id":"https://openalex.org/keywords/iterated-logarithm","display_name":"iterated logarithm","score":0.5509999990463257},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.8669999837875366},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.8820000290870667},{"id":"https://openalex.org/keywords/schauder-estimates","display_name":"Schauder estimates","score":0.7820000052452087},{"id":"https://openalex.org/keywords/uniqueness-in-law","display_name":"uniqueness in law","score":0.9520000219345093},{"id":"https://openalex.org/keywords/additive-functionals","display_name":"additive functionals","score":0.7450000047683716},{"id":"https://openalex.org/keywords/divergence-free-drift","display_name":"divergence-free drift","score":0.7720000147819519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8101000189781189},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6820999979972839},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6147000193595886},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5997999906539917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5817000269889832},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5121999979019165},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4997999966144562},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.435699999332428},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C104824951","wikidata":"https://www.wikidata.org/wiki/Q830124","display_name":"Girsanov theorem","level":3,"score":0.3416000008583069},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2775999903678894},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02022","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02022","pdf_url":"https://arxiv.org/pdf/2609.02022","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.02022","doi":"https://doi.org/10.48550/arxiv.2609.02022","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02022","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02022","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02022","pdf_url":"https://arxiv.org/pdf/2609.02022","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1428129756","display_name":null,"funder_award_id":"CRC 1283","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6767698131","display_name":null,"funder_award_id":"12131019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8401788687","display_name":null,"funder_award_id":"CRC 1283","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207746411.pdf","grobid_xml":"https://content.openalex.org/works/W7207746411.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1537937696","https://openalex.org/W1809232600","https://openalex.org/W1948961796","https://openalex.org/W1968956487","https://openalex.org/W1971502565","https://openalex.org/W1997134592","https://openalex.org/W1999832754","https://openalex.org/W2026968525","https://openalex.org/W2030702013","https://openalex.org/W2058441860","https://openalex.org/W2087661960","https://openalex.org/W2255848429","https://openalex.org/W2535419206","https://openalex.org/W2896600674","https://openalex.org/W2900249711","https://openalex.org/W2938709832","https://openalex.org/W3039315720","https://openalex.org/W3048824894","https://openalex.org/W3091375151","https://openalex.org/W4287554889","https://openalex.org/W4306158338","https://openalex.org/W4394721662","https://openalex.org/W4400667238","https://openalex.org/W4413913490"],"related_works":["https://openalex.org/W3112713630","https://openalex.org/W4400667238","https://openalex.org/W3014653104","https://openalex.org/W2950781839","https://openalex.org/W3010973362","https://openalex.org/W4306158338","https://openalex.org/W4413447152","https://openalex.org/W2769414242","https://openalex.org/W4400668325","https://openalex.org/W4400173504"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,46,58,99],"stochastic":[3,74],"differential":[4],"equation":[5],"$$d":[6],"X_t=b(t,X_t)d":[7],"t+\\sqrt{2}d":[8],"W_t$$":[9],"on":[10],"$\\mathbb":[11],"R^d$,":[12],"where":[13],"$b$":[14],"is":[15,57],"a":[16,38,62,73,87],"time-dependent,":[17],"divergence-free":[18],"distributional":[19,78],"drift":[20,48],"of":[21],"critical":[22],"H\u00f6lder--Besov":[23],"regularity":[24],"$-1$,":[25],"strengthened":[26],"by":[27,41],"an":[28,50],"iterated-logarithmic":[29],"correction.":[30],"For":[31,103],"every":[32],"initial":[33],"probability":[34],"law,":[35],"we":[36,109],"construct":[37],"weak":[39,96],"solution":[40],"smooth":[42],"approximation":[43],"and":[44,72,90],"realize":[45],"singular":[47],"as":[49],"additive":[51],"functional.":[52],"The":[53],"main":[54],"analytic":[55],"ingredient":[56],"Schauder":[59],"estimate":[60,82],"with":[61,67],"logarithmic":[63,69],"smallness":[64],"factor.":[65],"Combined":[66],"uniform":[68],"Krylov":[70,101],"estimates":[71],"substitution":[75],"formula":[76],"for":[77],"test":[79],"functions,":[80],"this":[81],"allows":[83],"us":[84],"to":[85],"apply":[86],"Zvonkin":[88],"transformation":[89],"prove":[91],"uniqueness":[92],"in":[93],"law":[94],"among":[95],"solutions":[97,104],"satisfying":[98,118],"corresponding":[100],"bounds.":[102],"starting":[105],"from":[106],"deterministic":[107],"points,":[108],"further":[110],"show":[111],"that":[112],"their":[113],"time-marginal":[114],"distributions":[115],"admit":[116],"densities":[117],"two-sided":[119],"Aronson-type":[120],"Gaussian":[121],"estimates.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}
