{"id":"https://openalex.org/W7204881761","doi":"https://doi.org/10.48550/arxiv.2608.31099","title":"On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels","display_name":"On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204881761","doi":"https://doi.org/10.48550/arxiv.2608.31099"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.31099","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31099","pdf_url":"https://arxiv.org/pdf/2608.31099","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/2608.31099","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114336498","display_name":"Emmanuel Gnabeyeu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4387155306","display_name":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation","ror":"https://ror.org/02vnd0e65","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4387155306"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gnabeyeu, Emmanuel","raw_affiliation_strings":["Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM) , UMR 8001 , Sorbonne Universit\u00e9 and","Universit\u00e9 Paris Cit\u00e9 , Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM) , UMR 8001 , Sorbonne Universit\u00e9 and","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4387155306"]},{"raw_affiliation_string":"Universit\u00e9 Paris Cit\u00e9 , Paris , France","institution_ids":["https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090083053","display_name":"Gilles Pag\u00e8s","orcid":"https://orcid.org/0000-0001-6487-3079","observed_orcids":["https://orcid.org/0000-0001-6487-3079"]},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4387155306","display_name":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation","ror":"https://ror.org/02vnd0e65","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4387155306"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pag\u00e8s, Gilles","raw_affiliation_strings":["Laboratoire de Probabilit\u00e9s,","Statistique et Mod\u00e9lisation (LPSM) , UMR 8001 , Sorbonne Universit\u00e9 , case 158 , 4 , pl. Jussieu , F-75252 Paris Cedex 5 , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Probabilit\u00e9s,","institution_ids":[]},{"raw_affiliation_string":"Statistique et Mod\u00e9lisation (LPSM) , UMR 8001 , Sorbonne Universit\u00e9 , case 158 , 4 , pl. Jussieu , F-75252 Paris Cedex 5 , France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4387155306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.9955999851226807,"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":0.9955999851226807,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.00139999995008111,"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":0.0008999999845400453,"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/stochastic-volterra-integral-equations","display_name":"stochastic Volterra integral equations","score":0.8790000081062317},{"id":"https://openalex.org/keywords/mean-reversion","display_name":"mean reversion","score":0.7160000205039978},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.699999988079071},{"id":"https://openalex.org/keywords/covariance-structure","display_name":"covariance structure","score":0.6990000009536743},{"id":"https://openalex.org/keywords/long-range-dependence","display_name":"long-range dependence","score":0.9190000295639038},{"id":"https://openalex.org/keywords/persistence","display_name":"persistence","score":0.4970000088214874},{"id":"https://openalex.org/keywords/finite-horizon","display_name":"finite horizon","score":0.4429999887943268}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7867000102996826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817000150680542},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7408999800682068},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5950999855995178},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5823000073432922},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.374099999666214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37290000915527344},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C20538924","wikidata":"https://www.wikidata.org/wiki/Q822139","display_name":"Characteristic function (probability theory)","level":3,"score":0.296999990940094},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.25450000166893005}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2608.31099","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31099","pdf_url":"https://arxiv.org/pdf/2608.31099","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":"pmh:oai:HAL:hal-05733278v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05733278v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2608.31099","doi":"https://doi.org/10.48550/arxiv.2608.31099","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31099","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:2608.31099","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31099","pdf_url":"https://arxiv.org/pdf/2608.31099","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/W7204881761.pdf","grobid_xml":"https://content.openalex.org/works/W7204881761.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1489022300","https://openalex.org/W4416019946","https://openalex.org/W7128733098","https://openalex.org/W7135062725","https://openalex.org/W7140178291","https://openalex.org/W7141578547","https://openalex.org/W7148805909","https://openalex.org/W7160162312"],"related_works":["https://openalex.org/W4416019946","https://openalex.org/W4416145215","https://openalex.org/W4391375220","https://openalex.org/W7141578547","https://openalex.org/W1976732971","https://openalex.org/W2795283210","https://openalex.org/W7212049630","https://openalex.org/W2741033083","https://openalex.org/W2018728740","https://openalex.org/W3215606952"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,28,38,44,50,61,66,86,93,111,121,131,162],"fake":[3],"stationarity":[4],"properties":[5],"of":[6,114,127,138,148],"solutions":[7,113],"to":[8,79,145],"forward":[9],"Stochastic":[10,150],"Volterra":[11,151],"Integral":[12,152],"Equations":[13,153],"(SVIEs)":[14],"with":[15,65],"affine":[16],"drift":[17],"and":[18,26,43,96,171],"long-memory":[19,116],"(regular)":[20],"kernels,":[21],"both":[22,109],"on":[23],"finite":[24],"horizons":[25],"in":[27,49,60,85,108,120,161],"long-run":[29],"regime.":[30],"By":[31],"either":[32],"deriving":[33],"explicit":[34],"closed-form":[35],"specifications":[36],"for":[37,135],"deterministic":[39,56],"initial":[40],"condition":[41],"$\u03d5$":[42],"mean-reversion":[45],"function":[46],"$\u03bc$":[47,70],"appearing":[48],"drift,":[51],"or":[52,177],"by":[53,155],"introducing":[54],"a":[55,81,100,125,146],"stabilizing":[57],"factor":[58],"$\u03c2$":[59],"diffusion":[62,139,169],"coefficient":[63],"associated":[64],"kernel":[67],"while":[68],"keeping":[69],"fully":[71],"flexible,":[72],"we":[73,104],"show":[74],"that":[75,88],"it":[76],"is":[77],"possible":[78],"induce":[80],"\\textit{fake":[82],"stationary}":[83],"regime,":[84],"sense":[87],"all":[89],"marginal":[90],"distributions":[91],"share":[92],"same":[94,132],"mean":[95],"variance.":[97],"Afterwards,":[98],"using":[99],"refined":[101],"asymptotic":[102],"analysis,":[103],"further":[105],"establish":[106],"that,":[107],"frameworks,":[110],"time-shifted":[112],"these":[115],"SVIEs":[117],"converge":[118],"weakly,":[119],"functional":[122],"sense,":[123],"toward":[124],"family":[126],"$L^2$-stationary":[128],"processes":[129],"sharing":[130],"covariance":[133],"structure,":[134],"suitable":[136],"classes":[137],"coefficients.":[140],"These":[141],"results":[142],"are":[143],"applied":[144],"class":[147],"exponential-fractional":[149],"driven":[154],"an":[156],"$\u03b1$-gamma":[157],"fractional":[158],"integration":[159],"kernel,":[160],"particular":[163],"regime":[164],"\\(\u03b1\\geq":[165],"1\\),":[166],"which":[167],"regularizes":[168],"paths":[170],"invoke":[172],"textit{":[173],"long-term":[174],"memory},":[175],"persistence":[176],"long":[178],"range":[179],"dependence.":[180]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}