{"id":"https://openalex.org/W2104635576","doi":"https://doi.org/10.1214/ejp.v8-166","title":"Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales","display_name":"Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2104635576","doi":"https://doi.org/10.1214/ejp.v8-166","mag":"2104635576"},"language":"en","primary_location":{"id":"doi:10.1214/ejp.v8-166","doi":"https://doi.org/10.1214/ejp.v8-166","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v8-166","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-8/issue-none/Approximation-at-First-and-Second-Order-of-m-order-Integrals/10.1214/EJP.v8-166.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-8/issue-none/Approximation-at-First-and-Second-Order-of-m-order-Integrals/10.1214/EJP.v8-166.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077949353","display_name":"Mihai Gradinaru","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4405264217","display_name":"Universit\u00e9 Henri Poincar\u00e9","ror":"https://ror.org/019wrwh65","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405264217","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mihai Gradinaru","raw_affiliation_strings":["Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e","Institut \u00c9lie Cartan de Nancy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I4405264217"]},{"raw_affiliation_string":"Institut \u00c9lie Cartan de Nancy","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075482281","display_name":"Ivan Nourdin","orcid":"https://orcid.org/0000-0002-8742-0723","observed_orcids":["https://orcid.org/0000-0002-8742-0723"]},"institutions":[{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210147464","https://openalex.org/I4387155306"]},{"id":"https://openalex.org/I4405264217","display_name":"Universit\u00e9 Henri Poincar\u00e9","ror":"https://ror.org/019wrwh65","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405264217","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ivan Nourdin","raw_affiliation_strings":["Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e","Institut \u00c9lie Cartan de Nancy","Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I4405264217"]},{"raw_affiliation_string":"Institut \u00c9lie Cartan de Nancy","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","institution_ids":["https://openalex.org/I4210147464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":675,"currency":"USD","value_usd":675},"apc_paid":{"value":675,"currency":"USD","value_usd":675},"fwci":2.2016,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.90706208,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":"none","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9965999722480774,"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":0.9965999722480774,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"fractional Brownian motion","score":0.9929999709129333},{"id":"https://openalex.org/keywords/hurst-exponent","display_name":"Hurst exponent","score":0.9049999713897705},{"id":"https://openalex.org/keywords/semimartingales","display_name":"semimartingales","score":0.9480000138282776},{"id":"https://openalex.org/keywords/malliavin-calculus","display_name":"Malliavin calculus","score":0.4650000035762787},{"id":"https://openalex.org/keywords/integral-approximation","display_name":"integral approximation","score":0.4779999852180481},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.8529999852180481},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.7820000052452087},{"id":"https://openalex.org/keywords/gaussian-moments","display_name":"Gaussian moments","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.851136326789856},{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.8166548013687134},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.7409529089927673},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6246522665023804},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6151122450828552},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5365310907363892},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4777218997478485},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.46474000811576843},{"id":"https://openalex.org/C2987636958","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic integral","level":3,"score":0.4411117136478424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42130231857299805},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35425350069999695},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.21223697066307068},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1214/ejp.v8-166","doi":"https://doi.org/10.1214/ejp.v8-166","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v8-166","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-8/issue-none/Approximation-at-First-and-Second-Order-of-m-order-Integrals/10.1214/EJP.v8-166.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},{"id":"pmh:oai:orbilu.uni.lu:10993/19304","doi":null,"is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/19304","pdf_url":"https://orbilu.uni.lu/bitstream/10993/19304/1/getdoc7e85.pdf","source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Probability, 8 (18), 1-26 (2003)","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:CULeuclid:euclid.ejp/1464037591","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ejp/1464037591","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:HAL:hal-00091322v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-00091322","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Probability, 2003, 8, pp.1-26","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1214/ejp.v8-166","doi":"https://doi.org/10.1214/ejp.v8-166","is_oa":true,"landing_page_url":"https://doi.org/10.1214/ejp.v8-166","pdf_url":"https://projecteuclid.org/journals/electronic-journal-of-probability/volume-8/issue-none/Approximation-at-First-and-Second-Order-of-m-order-Integrals/10.1214/EJP.v8-166.pdf","source":{"id":"https://openalex.org/S181633058","display_name":"Electronic Journal of Probability","issn_l":"1083-6489","issn":["1083-6489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2104635576.pdf","grobid_xml":"https://content.openalex.org/works/W2104635576.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W141291116","https://openalex.org/W1545370368","https://openalex.org/W1554577510","https://openalex.org/W1809232600","https://openalex.org/W1873708505","https://openalex.org/W1964702866","https://openalex.org/W1971235084","https://openalex.org/W1978094758","https://openalex.org/W1979083211","https://openalex.org/W1990795692","https://openalex.org/W1992472513","https://openalex.org/W2003427294","https://openalex.org/W2023575643","https://openalex.org/W2035925506","https://openalex.org/W2040324819","https://openalex.org/W2057112986","https://openalex.org/W2061630179","https://openalex.org/W2065240584","https://openalex.org/W2126001881","https://openalex.org/W2147576019","https://openalex.org/W4252123180","https://openalex.org/W4293510232"],"related_works":["https://openalex.org/W7100368020","https://openalex.org/W1600831658","https://openalex.org/W2014569746","https://openalex.org/W3021797414","https://openalex.org/W2061966562","https://openalex.org/W2087409596","https://openalex.org/W3162377055","https://openalex.org/W2030184595","https://openalex.org/W1528655171","https://openalex.org/W2040324819"],"abstract_inverted_index":{"Let":[0],"$X$":[1,132,155],"be":[2],"the":[3,36,39,45,70,85,89,102,110,125,134],"fractional":[4,135],"Brownian":[5,129,136,152],"motion":[6,130,137,153],"of":[7,38,44,52,55,65,84,88,117,138,147],"any":[8],"Hurst":[9],"index":[10,139],"$H\\in":[11,140],"(0,1)$":[12],"(resp.":[13,19],"a":[14,24,31,128,148,157],"semimartingale)":[15],"and":[16,27,80,142],"set":[17],"$\\alpha=H$":[18],"$\\alpha=\\frac{1}{2}$).":[20],"If":[21],"$Y$":[22,56],"is":[23,30,98,120,127,133,144,156],"continuous":[25],"process":[26],"if":[28,96],"$m$":[29,97],"positive":[32],"integer,":[33,101],"we":[34,67],"study":[35],"existence":[37],"limit,":[40],"as":[41,114],"$\\varepsilon\\rightarrow":[42,115],"0$,":[43,116],"approximations":[46],"$$":[47,51],"I_{\\varepsilon}(Y,X)":[48],":=\\left\\{\\int_{0}^{t}Y_{s}\\left(\\frac{X_{s+\\varepsilon}-X_{s}}{\\varepsilon^{\\alpha}}\\right)^{m}ds,\\,t\\geq":[49],"0\\right\\}":[50],"$m$-order":[53],"integral":[54],"with":[57],"respect":[58],"to":[59,105],"$X$.":[60],"For":[61],"these":[62],"two":[63,149],"choices":[64],"$X$,":[66],"prove":[68,123],"that":[69,124],"limits":[71],"are":[72,81],"almost":[73],"sure,":[74],"uniformly":[75],"on":[76],"each":[77],"compact":[78],"interval,":[79],"in":[82,112,145],"terms":[83],"$m$-th":[86],"moment":[87],"Gaussian":[90],"standard":[91,151],"random":[92],"variable.":[93],"In":[94,107],"particular,":[95],"an":[99],"odd":[100],"limit":[103,126],"equals":[104],"zero.":[106],"this":[108],"case,":[109],"convergence":[111],"distribution,":[113],"$\\varepsilon^{-\\frac{1}{2}}":[118],"I_{\\varepsilon}(1,X)$":[119],"studied.":[121],"We":[122],"when":[131,154],"(0,\\frac{1}{2}]$,":[141],"it":[143],"term":[146],"dimensional":[150],"semimartingale.":[158]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2016-06-24T00:00:00"}
