{"id":"https://openalex.org/W7164888599","doi":"https://doi.org/10.48550/arxiv.2606.15843","title":"Long-time Behaviour of DLRA for SDEs","display_name":"Long-time Behaviour of DLRA for SDEs","publication_year":2026,"publication_date":"2026-06-14","ids":{"openalex":"https://openalex.org/W7164888599","doi":"https://doi.org/10.48550/arxiv.2606.15843"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.15843","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15843","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.15843","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113790150","display_name":"Jianhai Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bao, Jianhai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138691154","display_name":"Haitao Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Haitao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138714176","display_name":"Yue Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yue","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/T12303","display_name":"Tensor decomposition and applications","score":0.2011999934911728,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T12303","display_name":"Tensor decomposition and applications","score":0.2011999934911728,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.1467999964952469,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.12870000302791595,"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/probability-measure","display_name":"Probability measure","score":0.6309000253677368},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6299999952316284},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.6134999990463257},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5702000260353088},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5163999795913696},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5019999742507935},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.47119998931884766},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.427700012922287},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.400299996137619}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202999830245972},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6309000253677368},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6299999952316284},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.6134999990463257},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5702000260353088},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5163999795913696},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5019999742507935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4997999966144562},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40070000290870667},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3799000084400177},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.32199999690055847},{"id":"https://openalex.org/C104824951","wikidata":"https://www.wikidata.org/wiki/Q830124","display_name":"Girsanov theorem","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C2776825372","wikidata":"https://www.wikidata.org/wiki/Q3922411","display_name":"Jump process","level":3,"score":0.30720001459121704},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C205301714","wikidata":"https://www.wikidata.org/wiki/Q228249","display_name":"Random measure","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.15843","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15843","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.15843","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15843","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,45,136],"study":[1],"dynamical":[2,170,182],"orthogonal":[3],"(DO)":[4],"approximations":[5,172],"of":[6,32,49,79,102,153,169,176,180],"stochastic":[7,43,62,181],"differential":[8,63],"equations":[9],"and":[10,25,40,54,65,92,126,149],"investigate":[11],"their":[12],"long-time":[13,177],"behaviour.":[14],"The":[15,112],"DO":[16,52,85,110],"formulation":[17],"represents":[18],"the":[19,37,47,50,60,70,77,84,96,100,108,133,140,151,167,174],"solution":[20],"by":[21],"a":[22,28,41,118,127,163],"low-rank":[23,67,142,171],"decomposition":[24],"leads":[26],"to":[27,131],"coupled":[29],"system":[30,53],"consisting":[31],"an":[33,103,122,145],"evolution":[34],"equation":[35,64],"on":[36,95],"Stiefel":[38],"manifold":[39],"reduced":[42],"process.":[44],"establish":[46],"well-posedness":[48],"strong":[51,109],"derive":[55],"quantitative":[56],"error":[57],"estimates":[58],"between":[59],"original":[61],"its":[66],"approximation":[68,175],"in":[69,173],"Wasserstein":[71],"distance.":[72],"Our":[73],"main":[74],"contribution":[75],"is":[76],"analysis":[78],"invariant":[80,104,146,154],"probability":[81,105,147],"measures":[82,155],"for":[83,107,121,166],"dynamics.":[86,135],"Under":[87],"suitable":[88],"dissipativity,":[89],"Lipschitz":[90],"continuity,":[91],"non-degeneracy":[93],"assumptions":[94],"coefficients,":[97],"we":[98],"prove":[99],"existence":[101],"measure":[106,148],"system.":[111],"proof":[113],"combines":[114],"uniform":[115],"moment":[116],"estimates,":[117],"Krylov--Bogoliubov":[119],"argument":[120],"associated":[123],"frozen":[124],"system,":[125],"Kakutani-Fan-Glicksberg":[128],"fixed-point":[129],"theorem":[130],"recover":[132],"self-consistent":[134],"further":[137],"show":[138],"that":[139],"induced":[141],"process":[143],"admits":[144],"discuss":[150],"structure":[152],"through":[156],"several":[157],"illustrative":[158],"examples.":[159],"These":[160],"results":[161],"provide":[162],"rigorous":[164],"foundation":[165],"use":[168],"statistical":[178],"properties":[179],"systems.":[183]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-17T00:00:00"}
