{"id":"https://openalex.org/W7220436792","doi":"https://doi.org/10.48550/arxiv.2610.03541","title":"An infinite-dimensional Skorokhod problem with a diagonalization approach","display_name":"An infinite-dimensional Skorokhod problem with a diagonalization approach","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220436792","doi":"https://doi.org/10.48550/arxiv.2610.03541"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03541","pdf_url":"https://arxiv.org/pdf/2610.03541","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":null,"license_id":null,"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/2610.03541","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136477185","display_name":"Louis T. Clarke","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]},{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Clarke, Louis T.","raw_affiliation_strings":["Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","Department of Mathematics , Iowa State University , Ames , IA 50011"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Mathematics , Iowa State University , Ames , IA 50011","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064855799","display_name":"Guodong Pang","orcid":"https://orcid.org/0000-0001-6468-0429","observed_orcids":["https://orcid.org/0000-0001-6468-0429"]},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]},{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pang, Guodong","raw_affiliation_strings":["Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","Department of Mathematics , Iowa State University , Ames , IA 50011"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Mathematics , Iowa State University , Ames , IA 50011","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157478319","display_name":"Ruoyu Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]},{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wu, Ruoyu","raw_affiliation_strings":["Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","Department of Mathematics , Iowa State University , Ames , IA 50011"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Applied Mathematics and Operations Research , George R. Brown School of Engineering and Computing , Rice University , Houston , TX 77005","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Mathematics , Iowa State University , Ames , IA 50011","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9409000277519226,"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":0.9409000277519226,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.038600001484155655,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0052999998442828655,"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/oblique-reflection","display_name":"oblique reflection","score":0.8149999976158142},{"id":"https://openalex.org/keywords/matrix-diagonalization","display_name":"diagonalization","score":0.8050000071525574},{"id":"https://openalex.org/keywords/cadlag-paths","display_name":"c\u00e0dl\u00e0g paths","score":0.7450000047683716},{"id":"https://openalex.org/keywords/l1-spaces","display_name":"L1 spaces","score":0.460999995470047},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7860000133514404},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.9470000267028809},{"id":"https://openalex.org/keywords/function-spaces","display_name":"function spaces","score":0.503000020980835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8776000142097473},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.8490999937057495},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5169000029563904},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.43630000948905945},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4260999858379364},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36320000886917114},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34610000252723694},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.2962999939918518},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03541","pdf_url":"https://arxiv.org/pdf/2610.03541","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03541","doi":"https://doi.org/10.48550/arxiv.2610.03541","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03541","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03541","pdf_url":"https://arxiv.org/pdf/2610.03541","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220436792.pdf","grobid_xml":"https://content.openalex.org/works/W7220436792.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7161734042"],"related_works":["https://openalex.org/W2133751250","https://openalex.org/W2949160638","https://openalex.org/W2207477202","https://openalex.org/W7099998182","https://openalex.org/W2075712204","https://openalex.org/W7097152388","https://openalex.org/W2009349041","https://openalex.org/W4411450616","https://openalex.org/W7117240757","https://openalex.org/W2047613145"],"abstract_inverted_index":{"We":[0,157],"study":[1,210],"an":[2,25,98,122],"infinite-dimensional":[3,99,200],"Skorokhod":[4,91,163,178,192],"problem":[5,92],"on":[6,37,74,93,104],"the":[7,51,55,63,79,88,94,105,126,130,134,161,175,199,209],"positive":[8,32,52,112],"cone":[9,64],"of":[10,82,125,133,149,190,198,211],"$L_1([0,1])$,":[11],"where":[12,78],"a":[13,17,31,68,110,117,182,195,206,222],"regulator":[14,56],"process":[15,47],"constrains":[16],"free":[18],"c\u00e0dl\u00e0g":[19],"path":[20],"to":[21,62,97,120,173],"remain":[22],"nonnegative":[23,95],"through":[24,116],"oblique":[26],"reflection":[27,201],"mechanism":[28],"determined":[29],"by":[30],"linear":[33,135],"integral":[34],"operator":[35,106,136],"$\\boldsymbol{F}$":[36,107],"$L_1([0,1])$":[38],"with":[39,60,171,215],"spectral":[40],"radius":[41],"less":[42,138],"than":[43,139],"$1$.":[44],"This":[45,85],"constrained":[46,212],"$Z$":[48,83],"remains":[49],"in":[50,128,229],"cone,":[53],"and":[54,66,147,168,177,220],"$Y$":[57],"is":[58,137,165],"nondecreasing":[59],"respect":[61,172],"order":[65],"satisfies":[67],"pointwise":[69],"complementarity":[70],"condition,":[71],"increasing":[72],"only":[73],"those":[75],"space-time":[76],"regions":[77],"corresponding":[80],"component":[81],"vanishes.":[84],"formulation":[86],"extends":[87],"classical":[89],"multidimensional":[90,191],"orthant":[96],"setting.":[100],"Under":[101],"suitable":[102],"assumptions":[103],"that":[108,160],"guarantee":[109],"dominant":[111],"eigenfunction,":[113],"we":[114,144],"proceed":[115],"diagonalization":[118],"argument":[119],"give":[121],"alternative":[123],"representation":[124],"system":[127],"which":[129],"$L_1$":[131],"norm":[132],"1.":[140],"From":[141],"this":[142],"characterization,":[143],"establish":[145],"existence":[146],"uniqueness":[148],"solutions":[150,184],"for":[151,208,224],"arbitrary":[152],"input":[153],"paths":[154],"$X\\in":[155],"D([0,T],L_1([0,1]))$.":[156],"further":[158],"show":[159],"associated":[162],"map":[164],"well":[166],"defined":[167],"Lipschitz":[169],"continuous":[170],"both":[174],"uniform":[176],"$J_1$":[179],"topologies.":[180],"As":[181],"consequence,":[183],"may":[185],"be":[186],"obtained":[187],"as":[188],"limits":[189],"problems,":[193],"providing":[194],"constructive":[196],"characterization":[197],"mechanism.":[202],"These":[203],"results":[204],"provide":[205,221],"framework":[207],"stochastic":[213,226],"systems":[214],"infinitely":[216],"many":[217],"interacting":[218],"components":[219],"foundation":[223],"reflected":[225],"processes":[227],"evolving":[228],"function":[230],"spaces.":[231]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}