{"id":"https://openalex.org/W2188965660","doi":"https://doi.org/10.30757/alea.v13-10","title":"A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences","display_name":"A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2188965660","doi":"https://doi.org/10.30757/alea.v13-10","mag":"2188965660"},"language":"en","primary_location":{"id":"doi:10.30757/alea.v13-10","doi":"https://doi.org/10.30757/alea.v13-10","is_oa":false,"landing_page_url":"https://doi.org/10.30757/alea.v13-10","pdf_url":null,"source":{"id":"https://openalex.org/S2475989817","display_name":"Latin American Journal of Probability and Mathematical Statistics","issn_l":"1980-0436","issn":["1980-0436"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-3","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Latin American Journal of Probability and Mathematical Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1603.00365","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082272979","display_name":"L\u00e9o Neufcourt","orcid":"https://orcid.org/0000-0002-0502-4429","observed_orcids":["https://orcid.org/0000-0002-0502-4429"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L\u00e9o Neufcourt","raw_affiliation_strings":["Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033321277","display_name":"Frederi G Viens","orcid":"https://orcid.org/0000-0001-9162-8212","observed_orcids":["https://orcid.org/0000-0001-9162-8212"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frederi G. Viens","raw_affiliation_strings":["PURDUE UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PURDUE UNIVERSITY","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0783,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.93237294,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"13","issue":"1","first_page":"239","last_page":"239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6176999807357788,"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":0.6176999807357788,"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/T11716","display_name":"Random Matrices and Applications","score":0.10809999704360962,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.10679999738931656,"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/fourth-moment-theorem","display_name":"fourth moment theorem","score":0.9520000219345093},{"id":"https://openalex.org/keywords/wiener-chaos","display_name":"Wiener chaos","score":0.8679999709129333},{"id":"https://openalex.org/keywords/stationary-gaussian-sequences","display_name":"stationary Gaussian sequences","score":0.8920000195503235},{"id":"https://openalex.org/keywords/quadratic-variation","display_name":"quadratic variation","score":0.8069999814033508},{"id":"https://openalex.org/keywords/cumulants","display_name":"cumulants","score":0.6819999814033508},{"id":"https://openalex.org/keywords/speed-of-convergence","display_name":"speed of convergence","score":0.8859999775886536},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"fractional Brownian motion","score":0.9890000224113464},{"id":"https://openalex.org/keywords/power-spectrum","display_name":"power spectrum","score":0.43700000643730164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8166036605834961},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.7095813155174255},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6073600649833679},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5866618156433105},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5556339621543884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5249804854393005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4994690418243408},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4908483624458313},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48735958337783813},{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.45943161845207214},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4428451955318451},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.44259604811668396},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4276023507118225},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.35160669684410095},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12065544724464417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09078171849250793},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08620795607566833},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.30757/alea.v13-10","doi":"https://doi.org/10.30757/alea.v13-10","is_oa":false,"landing_page_url":"https://doi.org/10.30757/alea.v13-10","pdf_url":null,"source":{"id":"https://openalex.org/S2475989817","display_name":"Latin American Journal of Probability and Mathematical Statistics","issn_l":"1980-0436","issn":["1980-0436"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-3","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Latin American Journal of Probability and Mathematical Statistics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1603.00365","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.00365","pdf_url":"https://arxiv.org/pdf/1603.00365","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":"mag:2188965660","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1603.00365.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.642.8269","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.642.8269","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.purdue.edu/~viens/publications/3m.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1603.00365","doi":"https://doi.org/10.48550/arxiv.1603.00365","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.00365","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:1603.00365","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.00365","pdf_url":"https://arxiv.org/pdf/1603.00365","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":[{"id":"https://openalex.org/G4367685131","display_name":"Density and tail estimates via Malliavin calculus, and applications","funder_award_id":"0907321","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322642","display_name":"Universidad de Valpara\u00edso","ror":"https://ror.org/00h9jrb69"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2188965660.pdf","grobid_xml":"https://content.openalex.org/works/W2188965660.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W48692188","https://openalex.org/W1554577510","https://openalex.org/W1924935520","https://openalex.org/W2002323426","https://openalex.org/W2006471730","https://openalex.org/W2023575643","https://openalex.org/W2082586613","https://openalex.org/W2100672112","https://openalex.org/W2100676242","https://openalex.org/W2106466894","https://openalex.org/W2126001881","https://openalex.org/W2130269141","https://openalex.org/W3099344973","https://openalex.org/W4292667882"],"related_works":["https://openalex.org/W2937635853","https://openalex.org/W2952953370","https://openalex.org/W1836611381","https://openalex.org/W4300226443","https://openalex.org/W2623106093","https://openalex.org/W7148335579","https://openalex.org/W2950086142","https://openalex.org/W7098228503","https://openalex.org/W2947340603","https://openalex.org/W3175257531"],"abstract_inverted_index":{"In":[0],"two":[1],"new":[2,236],"papers":[3],"(Bierme":[4],"et":[5],"al.,":[6],"2013)":[7],"and":[8,10,29,46,73,106,131,134,148,152,233],"(Nourdin":[9,130,151],"Peccati,":[11,30,132,153],"2015),":[12,133],"sharp":[13],"general":[14,122],"quantitative":[15,160],"bounds":[16,56],"\\":[17],"are":[18],"given":[19],"to":[20,41,53,83,114,141,158,248,250],"complement":[21],"the":[22,59,67,70,74,78,84,109,127,136,144,163,178,186,197,202,227,246,268,272],"well-known":[23],"fourth":[24,50,71,149],"moment":[25,80,100],"theorem":[26,101],"of":[27,61,65,69,77,86,129,139,143,165,170,180,188,199,216,224,267],"Nualart":[28],"by":[31,125],"which":[32,174],"a":[33,36,42,98,168,209,213,221,230,252,256,261],"sequence":[34],"in":[35,167,176,241],"fixed":[37],"Wiener":[38],"chaos":[39],"converges":[40,52],"normal":[43],"law":[44],"if":[45,48,105,108],"only":[47,107],"its":[49],"cumulant":[51,72],"$0$.":[54,115],"The":[55,239],"show":[57,96],"that":[58,97,245],"speed":[60,138,198],"convergence":[62,103,140,166,187,200,237,264],"is":[63,117,204,229,244,260],"precisely":[64],"order":[66,270],"maximum":[68],"absolute":[75],"value":[76],"third":[79,99,111,147],"(cumulant).":[81],"Specializing":[82],"case":[85,243],"normalized":[87],"centered":[88],"quadratic":[89,145,192],"variations":[90],"for":[91,119,162],"stationary":[92],"Gaussian":[93,206],"sequences,":[94],"we":[95,219,234],"holds:":[102],"occurs":[104],"sequence's":[110],"moments":[112],"tend":[113],"This":[116],"proved":[118],"sequences":[120],"with":[121],"decreasing":[123],"covariance,":[124],"using":[126],"result":[128,223],"finding":[135],"exact":[137],"$0$":[142],"variation's":[146],"cumulants.":[150],"2015)":[154],"also":[155,195],"allows":[156],"us":[157],"derive":[159],"estimates":[161],"speeds":[164],"class":[169,215],"log-modulated":[171,214],"covariance":[172],"structures,":[173],"puts":[175],"perspective":[177],"notion":[179],"critical":[181],"Hurst":[182],"parameter":[183],"when":[184,201],"studying":[185],"fractional":[189],"Brownian":[190],"motion's":[191],"variation.":[193],"We":[194],"study":[196],"limit":[203,228,254],"not":[205],"but":[207],"rather":[208],"second-Wiener-chaos":[210],"law.":[211],"Using":[212],"spectral":[217],"densities,":[218],"recover":[220],"classical":[222],"Dobrushin-Major/Taqqu":[225],"whereby":[226],"Rosenblatt":[231,253],"law,":[232],"provide":[235],"speeds.":[238],"conclusion":[240],"this":[242],"price":[247],"pay":[249],"obtain":[251],"despite":[255],"slowly":[257],"varying":[258],"modulation":[259],"very":[262],"slow":[263],"speed,":[265],"roughly":[266],"same":[269],"as":[271],"modulation.":[273]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
