{"id":"https://openalex.org/W7140083704","doi":"https://doi.org/10.48550/arxiv.2603.20089","title":"A new comparison principle for discrete Volterra equations with an application to convex sweeping processes with infinite delays","display_name":"A new comparison principle for discrete Volterra equations with an application to convex sweeping processes with infinite delays","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140083704","doi":"https://doi.org/10.48550/arxiv.2603.20089"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05594973v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05594973","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":"2026","raw_type":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.20089","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115646726","display_name":"Thierno Mamadou Bald\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bald\u00e9, Thierno Mamadou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076919061","display_name":"Vuk Mili\u0161i\u0107","orcid":"https://orcid.org/0000-0001-5530-2426"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Milisic, Vuk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003250568","display_name":"Steffen Plunder","orcid":"https://orcid.org/0000-0002-3371-3790"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Plunder, Steffen","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":false,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.5985000133514404,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.5985000133514404,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.06750000268220901,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.03269999846816063,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7186999917030334},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6782000064849854},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.557699978351593},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5349000096321106},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4805999994277954},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4717999994754791},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.43140000104904175},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4226999878883362},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4198000133037567},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.39649999141693115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7261999845504761},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7186999917030334},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6782000064849854},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.557699978351593},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5349000096321106},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4805999994277954},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46070000529289246},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4226999878883362},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3937000036239624},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.36329999566078186},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28600001335144043},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05594973v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05594973","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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2603.20089","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20089","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.20089","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20089","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,"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"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6919538378715515,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Comparison":[0],"principles":[1,11],"for":[2,85],"Volterra":[3,51],"equations":[4],"play":[5],"a":[6,79,90,122,125,130,201],"role":[7],"analogous":[8],"to":[9,26,95,139,183,207],"maximum":[10],"in":[12,63,70,93,102,147],"PDEs:":[13],"they":[14],"provide":[15],"positivity":[16],"and":[17,23,49,53,151],"stability":[18],"information":[19],"on":[20,41,173],"the":[21,28,34,64,103,118,148,154,157,162,166,170,174,177,184,190,197,208,215,224],"solution":[22],"allow":[24],"one":[25],"control":[27],"output":[29],"of":[30,98,114,120,156,169,176],"bounded":[31],"inputs.":[32],"In":[33,124,161],"continuous":[35],"setting,":[36],"such":[37,121],"results":[38],"often":[39],"rely":[40],"Laplace-transform":[42],"or":[43,72],"spectral":[44],"methods":[45],"(see":[46],"Gripenberg,":[47],"Londen,":[48],"Staffans,":[50],"Integral":[52],"Functional":[54],"Equations,":[55],"1990).":[56],"However,":[57],"these":[58],"tools":[59],"are":[60],"not":[61],"uniform":[62,83],"discretization":[65,191],"step":[66,127],"$h$":[67],"hence":[68],"fail":[69],"discrete":[71,149],"semi-discrete":[73],"approximations.":[74],"The":[75,142],"present":[76],"note":[77],"introduces":[78],"resolvent-free":[80],"argument":[81,143],"yielding":[82],"$L^\\infty(0,T)$-bounds":[84],"non-negative":[86],"kernels.":[87],"Compactness":[88],"is":[89,107,136,144,189],"key":[91],"ingredient":[92],"order":[94],"show":[96,129,213],"existence":[97],"sweeping":[99,164],"processes.":[100],"While":[101],"classical":[104,163],"framework":[105],"it":[106],"well":[108],"established,":[109],"adding":[110],"an":[111],"infinite":[112],"distribution":[113],"delays":[115],"complicates":[116],"greatly":[117],"obtaining":[119],"result.":[123],"first":[126],"we":[128],"general":[131],"energy":[132],"decay":[133],"estimate,":[134],"which":[135],"then":[137],"used":[138],"establish":[140],"compactness.":[141],"carried":[145],"out":[146],"setting":[150],"that":[152,214],"necessitates":[153],"introduction":[155],"new":[158],"comparison":[159],"principle.":[160],"process":[165],"previous":[167],"position":[168],"particle":[171],"lies":[172],"boundary":[175],"constraint":[178,209],"set,":[179],"staying":[180],"$O(h)$":[181],"close":[182],"next":[185],"projection":[186],"point":[187,217],"($h$":[188],"step).":[192],"Our":[193],"delay":[194],"model":[195],"projects":[196],"particle's":[198],"averaged":[199],"(by":[200],"unit":[202],"measure":[203],"kernel)":[204],"past":[205],"positions":[206],"set.":[210],"Numerical":[211],"simulations":[212],"projected":[216],"can":[218],"lie":[219],"at":[220],"$O(1)$":[221],"distance":[222],"from":[223],"convex":[225],"set's":[226],"boundary.":[227]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-24T00:00:00"}