{"id":"https://openalex.org/W3017772014","doi":"https://doi.org/10.1137/18m122666x","title":"Viscosity Solutions of Path-Dependent PDEs with Randomized Time","display_name":"Viscosity Solutions of Path-Dependent PDEs with Randomized Time","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3017772014","doi":"https://doi.org/10.1137/18m122666x","mag":"3017772014"},"language":"en","primary_location":{"id":"doi:10.1137/18m122666x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m122666x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","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/A5044750709","display_name":"Zhenjie Ren","orcid":"https://orcid.org/0000-0003-4656-4074"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Zhenjie Ren","raw_affiliation_strings":["CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)"],"affiliations":[{"raw_affiliation_string":"CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026739567","display_name":"Mauro Rosestolato","orcid":"https://orcid.org/0000-0002-0049-0092"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mauro Rosestolato","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044750709"],"corresponding_institution_ids":["https://openalex.org/I171048554"],"apc_list":null,"apc_paid":null,"fwci":3.4982,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.93286321,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"2","first_page":"1943","last_page":"1979"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9973999857902527,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.8624705076217651},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.7726060152053833},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.6610763669013977},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6583173274993896},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6495121717453003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5053642392158508},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.46428146958351135},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43921923637390137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3487269878387451},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.060227811336517334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0500202476978302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.043447256088256836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8624705076217651},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.7726060152053833},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.6610763669013977},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6583173274993896},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6495121717453003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5053642392158508},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.46428146958351135},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43921923637390137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3487269878387451},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.060227811336517334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0500202476978302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.043447256088256836},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m122666x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m122666x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03909160v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03909160","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2020, 52 (2), pp.1943-1979. ⟨10.1137/18M122666X⟩","raw_type":"Journal articles"},{"id":"pmh:oai:iris.unige.it:11567/1119743","is_oa":false,"landing_page_url":"https://hdl.handle.net/11567/1119743","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2712932445","display_name":null,"funder_award_id":"321111","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1560735985","https://openalex.org/W1971594473","https://openalex.org/W2012244785","https://openalex.org/W2018201955","https://openalex.org/W2018706083","https://openalex.org/W2032316144","https://openalex.org/W2136011614","https://openalex.org/W2143365754","https://openalex.org/W2161582152","https://openalex.org/W2565858504","https://openalex.org/W2749408143","https://openalex.org/W2962718871","https://openalex.org/W2962917010","https://openalex.org/W2962944597","https://openalex.org/W2963078692","https://openalex.org/W2963361196","https://openalex.org/W2963748055","https://openalex.org/W3101566353","https://openalex.org/W3102177650","https://openalex.org/W4230022934","https://openalex.org/W4297854194"],"related_works":["https://openalex.org/W2088353628","https://openalex.org/W1995876016","https://openalex.org/W2766367749","https://openalex.org/W2967599161","https://openalex.org/W2061417420","https://openalex.org/W4311111126","https://openalex.org/W3173219668","https://openalex.org/W3001427599","https://openalex.org/W2011375692","https://openalex.org/W2980424366"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,15,50,55],"new":[3,35],"definition":[4,20],"of":[5,18,68,80,86],"viscosity":[6,69,78,84],"solution":[7],"to":[8],"path-dependent":[9,81],"partial":[10,87],"differential":[11,88],"equations,":[12],"which":[13],"is":[14],"slight":[16],"modification":[17],"the":[19,34,39,47,66,72],"introduced":[21],"in":[22,46],"[I.":[23],"Ekren":[24],"et":[25],"al.,":[26],"Ann.":[27],"Probab.,":[28],"42":[29],"(2014),":[30],"pp.":[31],"204--236].":[32],"With":[33],"definition,":[36],"we":[37,64,76],"prove":[38,65],"two":[40],"important":[41],"results,":[42],"until":[43],"now":[44],"missing":[45],"literature,":[48],"namely,":[49],"general":[51],"stability":[52],"result":[53,57],"and":[54],"comparison":[56],"for":[58],"semicontinuous":[59],"sub-/supersolutions.":[60],"As":[61],"an":[62],"application,":[63],"existence":[67],"solutions":[70,79,85],"using":[71],"Perron":[73],"method.":[74],"Moreover,":[75],"connect":[77],"PDEs":[82],"with":[83],"equations":[89],"on":[90],"Hilbert":[91],"spaces.":[92]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}