{"id":"https://openalex.org/W2903832574","doi":"https://doi.org/10.1137/19m1237429","title":"Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities","display_name":"Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2903832574","doi":"https://doi.org/10.1137/19m1237429","mag":"2903832574"},"language":"en","primary_location":{"id":"doi:10.1137/19m1237429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1237429","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1812.05174","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jeremiah Birrell","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeremiah Birrell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Luc Rey-Bellet","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luc Rey-Bellet","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.418,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.58843865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"8","issue":"2","first_page":"539","last_page":"572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.13359999656677246,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.13359999656677246,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.09369999915361404,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.0925000011920929,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.6837000250816345},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.6008999943733215},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5570999979972839},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5163000226020813},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.46869999170303345},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.38690000772476196},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.3158000111579895}],"concepts":[{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.6837000250816345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.633400022983551},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5570999979972839},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47870001196861267},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.46869999170303345},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4668999910354614},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C177803969","wikidata":"https://www.wikidata.org/wiki/Q29205","display_name":"Uncertainty analysis","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27309998869895935},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.2718000113964081},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.2671999931335449},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.2637999951839447}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1237429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1237429","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1812.05174","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.05174","pdf_url":"https://arxiv.org/pdf/1812.05174","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1812.05174","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.05174","pdf_url":"https://arxiv.org/pdf/1812.05174","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2416061413","display_name":null,"funder_award_id":"FA-9550-18-1-0214","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5435160259","display_name":null,"funder_award_id":"DMS-1515712","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1567236254","https://openalex.org/W1693992350","https://openalex.org/W1882631872","https://openalex.org/W1946361304","https://openalex.org/W1964607942","https://openalex.org/W1976418263","https://openalex.org/W1977657887","https://openalex.org/W1995600142","https://openalex.org/W1999286169","https://openalex.org/W2003268963","https://openalex.org/W2010470683","https://openalex.org/W2014248834","https://openalex.org/W2031467591","https://openalex.org/W2063530260","https://openalex.org/W2068609910","https://openalex.org/W2076500319","https://openalex.org/W2077810240","https://openalex.org/W2118830699","https://openalex.org/W2131940723","https://openalex.org/W2148980794","https://openalex.org/W2151299863","https://openalex.org/W2164227042","https://openalex.org/W2166461660","https://openalex.org/W2355724939","https://openalex.org/W2565130142","https://openalex.org/W2593651454","https://openalex.org/W2962881065","https://openalex.org/W2963703812","https://openalex.org/W2963867712","https://openalex.org/W2964282829","https://openalex.org/W3123065937"],"related_works":[],"abstract_inverted_index":{"Information-theory":[0],"based":[1],"variational":[2,32],"principles":[3],"have":[4],"proven":[5],"effective":[6],"at":[7],"providing":[8],"scalable":[9],"uncertainty":[10,44],"quantification":[11,45],"(i.e.,":[12],"robustness)":[13],"bounds":[14,46,62],"for":[15,47],"quantities":[16],"of":[17,22,74],"interest":[18],"in":[19,66],"the":[20,67],"presence":[21],"nonparametric":[23],"model-form":[24],"uncertainty.":[25],"In":[26],"this":[27],"work,":[28],"we":[29],"combine":[30],"such":[31],"formulas":[33],"with":[34],"functional":[35],"inequalities":[36],"(Poincar\u00e9,":[37],"$\\log$-Sobolev,":[38],"Liapunov":[39],"functions)":[40],"to":[41,54,72],"derive":[42],"explicit":[43],"time-averaged":[48],"observables,":[49],"comparing":[50],"a":[51,55],"Markov":[52,79],"process":[53],"second":[56],"(not":[57],"necessarily":[58],"Markov)":[59],"process.":[60],"These":[61],"are":[63],"well":[64],"behaved":[65],"infinite-time":[68],"limit":[69],"and":[70,77],"apply":[71],"steady-states":[73],"both":[75],"discrete":[76],"continuous-time":[78],"processes.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2018-12-22T00:00:00"}