{"id":"https://openalex.org/W2114457482","doi":"https://doi.org/10.1214/ejp.v16-950","title":"Quasi-sure Stochastic Analysis through Aggregation","display_name":"Quasi-sure Stochastic Analysis through Aggregation","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2114457482","doi":"https://doi.org/10.1214/ejp.v16-950","mag":"2114457482"},"language":"en","primary_location":{"id":"doi:10.1214/ejp.v16-950","doi":"https://doi.org/10.1214/ejp.v16-950","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v16-950","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-16/issue-none/Quasi-sure-Stochastic-Analysis-through-Aggregation/10.1214/EJP.v16-950.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-16/issue-none/Quasi-sure-Stochastic-Analysis-through-Aggregation/10.1214/EJP.v16-950.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022412598","display_name":"Halil Mete Soner","orcid":"https://orcid.org/0000-0002-0824-1808","observed_orcids":["https://orcid.org/0000-0002-0824-1808"]},"institutions":[{"id":"https://openalex.org/I54157616","display_name":"Swiss Finance Institute","ror":"https://ror.org/02cgn2a44","country_code":"CH","type":"education","lineage":["https://openalex.org/I54157616"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mete Soner","raw_affiliation_strings":["Swiss Finance Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Swiss Finance Institute","institution_ids":["https://openalex.org/I54157616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105990961","display_name":"Nizar Touzi","orcid":"https://orcid.org/0000-0001-5252-033X","observed_orcids":["https://orcid.org/0000-0001-5252-033X"]},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nizar Touzi","raw_affiliation_strings":["Ecole Polytechnique Paris"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique Paris","institution_ids":["https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100374711","display_name":"Jianfeng Zhang","orcid":"https://orcid.org/0000-0002-3591-3219","observed_orcids":["https://orcid.org/0000-0002-3591-3219"]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianfeng Zhang","raw_affiliation_strings":["University of Southern California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":675,"currency":"USD","value_usd":675},"apc_paid":{"value":675,"currency":"USD","value_usd":675},"fwci":37.2074,"has_fulltext":true,"cited_by_count":172,"citation_normalized_percentile":{"value":0.99657684,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"16","issue":"none","first_page":"1844","last_page":"1879"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9916999936103821,"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":0.9916999936103821,"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":0.0027000000700354576,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.00139999995008111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/aggregation","display_name":"aggregation","score":0.6769999861717224},{"id":"https://openalex.org/keywords/fully-nonlinear-equations","display_name":"fully nonlinear equations","score":0.8069999814033508},{"id":"https://openalex.org/keywords/probabilistic-representation","display_name":"probabilistic representation","score":0.8050000071525574},{"id":"https://openalex.org/keywords/mathematical-finance","display_name":"financial mathematics","score":0.6549999713897705},{"id":"https://openalex.org/keywords/capacity-theory","display_name":"capacity theory","score":0.6869999766349792},{"id":"https://openalex.org/keywords/density","display_name":"density","score":0.597000002861023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8173292875289917},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7675129175186157},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6234604120254517},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6055546402931213},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5987287759780884},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5515937805175781},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5409278869628906},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5183019042015076},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5053220391273499},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4815152585506439},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.4515012800693512},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4474338889122009},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.41939088702201843},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4146900475025177},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41110625863075256},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3595288395881653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2614889144897461},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1258770227432251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11315310001373291},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1214/ejp.v16-950","doi":"https://doi.org/10.1214/ejp.v16-950","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v16-950","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-16/issue-none/Quasi-sure-Stochastic-Analysis-through-Aggregation/10.1214/EJP.v16-950.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/28169","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/28169","pdf_url":"http://hdl.handle.net/20.500.11850/28169","source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"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":"Electronic Journal of Probability, 16","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.2704","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.2704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1003.4431.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.ejp/1464820236","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ejp/1464820236","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.3929/ethz-b-000028169","doi":"https://doi.org/10.3929/ethz-b-000028169","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000028169","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"}],"best_oa_location":{"id":"doi:10.1214/ejp.v16-950","doi":"https://doi.org/10.1214/ejp.v16-950","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v16-950","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-16/issue-none/Quasi-sure-Stochastic-Analysis-through-Aggregation/10.1214/EJP.v16-950.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2388941477","display_name":"Mathematical Methods for Financial Risk Management","funder_award_id":"228053","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G4810840046","display_name":"Collaborative Research: Applications of Stochastic Analysis to Models of Multi-Agent Interactions","funder_award_id":"1008873","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308668","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60"},{"id":"https://openalex.org/F4320316296","display_name":"Swiss Finance Institute","ror":"https://ror.org/02cgn2a44"},{"id":"https://openalex.org/F4320331267","display_name":"Fondation du Risque","ror":"https://ror.org/01c3q7502"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2114457482.pdf","grobid_xml":"https://content.openalex.org/works/W2114457482.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W649943522","https://openalex.org/W1523471994","https://openalex.org/W1552064164","https://openalex.org/W1558902221","https://openalex.org/W1580561995","https://openalex.org/W1984328418","https://openalex.org/W1992382156","https://openalex.org/W1997901650","https://openalex.org/W2006080424","https://openalex.org/W2019443855","https://openalex.org/W2021318678","https://openalex.org/W2067773920","https://openalex.org/W2120900212","https://openalex.org/W2125555288","https://openalex.org/W2129969123","https://openalex.org/W2137282451","https://openalex.org/W2155429742","https://openalex.org/W2164282683","https://openalex.org/W2168474627","https://openalex.org/W2951112359"],"related_works":["https://openalex.org/W7096039893","https://openalex.org/W409796616","https://openalex.org/W2974479744","https://openalex.org/W1975518107","https://openalex.org/W1553748547","https://openalex.org/W2067969315","https://openalex.org/W7096996388","https://openalex.org/W2291247895","https://openalex.org/W138191857","https://openalex.org/W2007117584"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"on":[3,50,58],"developing":[4],"stochastic":[5],"analysis":[6],"simultaneously":[7],"under":[8],"a":[9,20,101,109],"general":[10],"family":[11,111,132],"of":[12,34,79,88,104,112],"probability":[13,22,114],"measures":[14],"that":[15],"are":[16],"not":[17],"dominated":[18],"by":[19],"single":[21],"measure.":[23],"The":[24,45],"interest":[25],"in":[26,86,126],"this":[27,94,98],"question":[28,99],"originates":[29],"from":[30],"the":[31,51,59,69,75,80,89,130],"probabilistic":[32],"representations":[33],"fully":[35],"nonlinear":[36,61],"partial":[37,62],"differential":[38,63],"equations":[39],"and":[40,55,83],"applications":[41],"to":[42,122],"mathematical":[43],"finance.":[44],"existing":[46],"literature":[47],"relies":[48],"either":[49],"capacity":[52],"theory":[53,71],"(Denis":[54],"Martini),":[56],"or":[57],"underlying":[60,90],"equation":[64],"(Peng).":[65],"In":[66,93],"both":[67],"approaches,":[68],"resulting":[70],"requires":[72],"certain":[73],"smoothness,":[74],"so-called":[76],"quasi-sure":[77],"continuity,":[78],"corresponding":[81],"processes":[82],"random":[84],"variables":[85],"terms":[87],"canonical":[91],"process.":[92],"paper,":[95],"we":[96],"investigate":[97],"for":[100],"larger":[102],"class":[103],"``non-smooth\"":[105],"processes,":[106,118],"but":[107],"with":[108],"restricted":[110,131],"non-dominated":[113],"measures.":[115],"For":[116],"smooth":[117],"our":[119],"approach":[120],"leads":[121],"similar":[123],"results":[124],"as":[125],"previous":[127],"literature,":[128],"provided":[129],"satisfies":[133],"an":[134],"additional":[135],"density":[136],"property.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":26},{"year":2012,"cited_by_count":10}],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2016-06-24T00:00:00"}