{"id":"https://openalex.org/W7224939811","doi":"https://doi.org/10.48550/arxiv.2610.39492","title":"Weighted Harris--oscillation contraction and invariant expectations for nonlinear Markov semigroups","display_name":"Weighted Harris--oscillation contraction and invariant expectations for nonlinear Markov semigroups","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224939811","doi":"https://doi.org/10.48550/arxiv.2610.39492"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39492","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39492","pdf_url":"https://arxiv.org/pdf/2610.39492","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39492","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160171553","display_name":"Danyang Zhao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao, Danyang","raw_affiliation_strings":["School of Mathematics , Shandong University , Jinan 250100 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Shandong University , Jinan 250100 , China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159983294","display_name":"Huaizhong Zhao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Zhao, Huaizhong","raw_affiliation_strings":["Department of Mathematical Sciences , Durham University , Durham DH1 3LE , United Kingdom ; and","School of Mathematics , Shandong University , Jinan 250100 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Durham University , Durham DH1 3LE , United Kingdom ; and","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"School of Mathematics , Shandong University , Jinan 250100 , China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"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":0.4417000114917755,"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":0.4417000114917755,"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":0.19210000336170197,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.11050000041723251,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-semigroups","display_name":"Markov semigroups","score":0.8330000042915344},{"id":"https://openalex.org/keywords/lyapunov-drift","display_name":"Lyapunov drift","score":0.8299999833106995},{"id":"https://openalex.org/keywords/parabolic-harnack-inequality","display_name":"parabolic Harnack inequality","score":0.8799999952316284},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.8429999947547913},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"multiplicative noise","score":0.6449999809265137},{"id":"https://openalex.org/keywords/viscosity-solutions","display_name":"viscosity solutions","score":0.5920000076293945},{"id":"https://openalex.org/keywords/ergodicity","display_name":"ergodicity","score":0.8790000081062317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8888999819755554},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.6902999877929688},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5045999884605408},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4643999934196472},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.39980000257492065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37470000982284546},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.34200000762939453},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3142000138759613},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.29739999771118164},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C2775958659","wikidata":"https://www.wikidata.org/wiki/Q5165690","display_name":"Contraction principle","level":3,"score":0.26420000195503235},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.2565999925136566},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39492","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39492","pdf_url":"https://arxiv.org/pdf/2610.39492","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.2610.39492","doi":"https://doi.org/10.48550/arxiv.2610.39492","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39492","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:2610.39492","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39492","pdf_url":"https://arxiv.org/pdf/2610.39492","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224939811.pdf","grobid_xml":"https://content.openalex.org/works/W7224939811.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7164883047","https://openalex.org/W2016473325","https://openalex.org/W2966987630","https://openalex.org/W4416190325","https://openalex.org/W2050184610","https://openalex.org/W3047428495","https://openalex.org/W4390354974","https://openalex.org/W1491534511","https://openalex.org/W1660107904","https://openalex.org/W4386043814"],"abstract_inverted_index":{"We":[0],"establish":[1],"a":[2,18,23,30,85,89,93,123,137,156],"weighted":[3,90,103],"contraction":[4,26,79,87,211],"principle":[5],"for":[6,106,119,165],"sublinear":[7,96],"Markov":[8],"semigroups":[9],"on":[10,29],"noncompact":[11],"state":[12,129],"spaces.":[13],"Its":[14],"abstract":[15,161],"inputs":[16],"are":[17,193,202],"Lyapunov":[19,31,82,112],"drift":[20,83,179,198],"condition":[21],"and":[22,55,64,69,102,134,136,173,199,201,212,227],"strict":[24,86],"local":[25,77],"of":[27,215,225],"oscillations":[28],"sublevel":[32],"set.":[33],"For":[34,187],"locally":[35,167],"uniformly":[36,168,204],"parabolic":[37,47],"diffusion":[38],"semigroups,":[39],"the":[40,46,52,67,75,81,99,111,174,188,191,196,210,216,223],"latter":[41],"is":[42,163],"obtained":[43],"by":[44,110],"applying":[45],"Harnack":[48],"inequality":[49],"to":[50],"both":[51],"upper":[53,68],"evolution":[54],"its":[56],"conjugate":[57],"lower":[58,70],"evolution:":[59],"if":[60],"$u=T_t\u03c6$,":[61],"then":[62,146],"$u-m$":[63],"$M-u$":[65],"solve":[66],"Bellman":[71],"equations,":[72],"respectively.":[73],"Combining":[74],"resulting":[76],"oscillation":[78,91],"with":[80,132,177],"yields":[84],"in":[88,98,222],"seminorm,":[92],"unique":[94],"invariant":[95],"expectation":[97],"finite-Lyapunov-moment":[100],"class,":[101],"exponential":[104],"convergence":[105],"Borel":[107,117],"observables":[108],"controlled":[109],"function.":[113],"To":[114],"treat":[115],"bounded":[116],"data":[118],"$G$-SDEs,":[120,172],"we":[121],"use":[122],"canonical":[124],"covariance-law":[125],"representation,":[126],"progressively":[127],"measurable":[128],"maps":[130],"compatible":[131],"conditioning":[133],"pasting,":[135],"stopped":[138],"dynamic":[139],"programming":[140],"principle.":[141],"A":[142],"probabilistic":[143],"Krylov--Safonov":[144],"argument":[145],"gives":[147],"positive-time":[148],"H\u00f6lder":[149],"regularisation":[150],"before":[151],"viscosity":[152],"identification,":[153],"thereby":[154],"avoiding":[155],"measurable-data":[157],"envelope":[158],"argument.":[159],"The":[160],"result":[162],"verified":[164],"ordinary":[166],"elliptic":[169],"SDEs,":[170],"multiplicative":[171],"full":[175,189],"equation":[176,190],"quadratic-variation":[178],"\\[":[180],"dX_t=b(X_t)\\,dt":[181],"+\\sum_{i,j=1}^m":[182],"h_{ij}(X_t)\\,d\\langle":[183],"B^i,B^j\\rangle_t":[184],"+\\sum_{j=1}^m\u03c3_j(X_t)\\,dB_t^j.":[185],"\\]":[186],"hypotheses":[192],"expressed":[194],"through":[195],"effective":[197],"covariance":[200,207],"required":[203],"over":[205],"all":[206],"scenarios.":[208],"Finally,":[209],"stochastic":[213],"continuity":[214],"associated":[217],"stationary":[218],"process":[219],"yield":[220],"ergodicity":[221],"sense":[224],"Feng":[226],"Zhao.":[228]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}