{"id":"https://openalex.org/W4411613145","doi":"https://doi.org/10.1017/jpr.2025.19","title":"Rates for the SLLN for long-memory and heavy-tailed processes","display_name":"Rates for the SLLN for long-memory and heavy-tailed processes","publication_year":2025,"publication_date":"2025-06-24","ids":{"openalex":"https://openalex.org/W4411613145","doi":"https://doi.org/10.1017/jpr.2025.19"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.19","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.19","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031388022","display_name":"Samir Ben Hariz","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108471","display_name":"Le Mans Universit\u00e9","ror":"https://ror.org/01mtcc283","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210108471"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Samir Ben Hariz","raw_affiliation_strings":["Universit\u00e9 du Maine","LMM - Laboratoire Manceau de Math\u00e9matiques (Le Mans Universit\u00e9 - Facult\u00e9 des Sciences et Techniques\r\nAvenue Olivier Messiaen - 72085 Le Mans Cedex 9 (France) - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 du Maine","institution_ids":[]},{"raw_affiliation_string":"LMM - Laboratoire Manceau de Math\u00e9matiques (Le Mans Universit\u00e9 - Facult\u00e9 des Sciences et Techniques\r\nAvenue Olivier Messiaen - 72085 Le Mans Cedex 9 (France) - France)","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4210108471"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026925187","display_name":"Salim Bouzebda","orcid":"https://orcid.org/0000-0001-7801-4945"},"institutions":[{"id":"https://openalex.org/I102516824","display_name":"Universit\u00e9 de Technologie de Compi\u00e8gne","ror":"https://ror.org/04y5kwa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I102516824"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Salim Bouzebda","raw_affiliation_strings":["Universit\u00e9 de technologie de Compi\u00e8gne","LMAC - Laboratoire de Math\u00e9matiques Appliqu\u00e9es de Compi\u00e8gne (Universit\u00e9 de Technologie de Compi\u00e8gne - Centre de Recherche de Royallieu - rue du Docteur Schweitzer- CS 60319 - 60203 COMPIEGNE Cedex - France)"],"raw_orcid":"https://orcid.org/0000-0001-7801-4945","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de technologie de Compi\u00e8gne","institution_ids":["https://openalex.org/I102516824"]},{"raw_affiliation_string":"LMAC - Laboratoire de Math\u00e9matiques Appliqu\u00e9es de Compi\u00e8gne (Universit\u00e9 de Technologie de Compi\u00e8gne - Centre de Recherche de Royallieu - rue du Docteur Schweitzer- CS 60319 - 60203 COMPIEGNE Cedex - France)","institution_ids":["https://openalex.org/I102516824"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026925187","https://openalex.org/A5031388022"],"corresponding_institution_ids":["https://openalex.org/I102516824","https://openalex.org/I4210108471","https://openalex.org/I4210155549"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15848025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"62","issue":"4","first_page":"1513","last_page":"1533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9905999898910522,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9847999811172485,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.815679669380188},{"id":"https://openalex.org/keywords/long-memory","display_name":"Long memory","score":0.4809491038322449},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3683040738105774},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3451552987098694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.815679669380188},{"id":"https://openalex.org/C2986394398","wikidata":"https://www.wikidata.org/wiki/Q1805477","display_name":"Long memory","level":3,"score":0.4809491038322449},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3683040738105774},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3451552987098694},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/jpr.2025.19","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.19","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05129242v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05129242","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Probability, 2025, pp.1-21. &#x27E8;10.1017/jpr.2025.19&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W87927865","https://openalex.org/W1508427692","https://openalex.org/W1968239790","https://openalex.org/W1970669268","https://openalex.org/W1973047053","https://openalex.org/W1974606612","https://openalex.org/W1989642436","https://openalex.org/W2001089051","https://openalex.org/W2019347082","https://openalex.org/W2023575643","https://openalex.org/W2039071135","https://openalex.org/W2041430578","https://openalex.org/W2042076461","https://openalex.org/W2047679099","https://openalex.org/W2047984191","https://openalex.org/W2060599345","https://openalex.org/W2083947137","https://openalex.org/W2086768018","https://openalex.org/W2100676242","https://openalex.org/W2109333856","https://openalex.org/W2136516258","https://openalex.org/W2158044918","https://openalex.org/W2269297145","https://openalex.org/W2314015410","https://openalex.org/W2314909683","https://openalex.org/W2602092929","https://openalex.org/W2789790663","https://openalex.org/W2802739963","https://openalex.org/W2963609774","https://openalex.org/W3039641802","https://openalex.org/W3101545912","https://openalex.org/W3103171473","https://openalex.org/W4247705294"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2000531222","https://openalex.org/W2029770004"],"abstract_inverted_index":{"Abstract":[0],"The":[1,96],"present":[2],"paper":[3],"develops":[4],"a":[5,40,54,62],"unified":[6],"approach":[7],"when":[8],"dealing":[9],"with":[10,16,24],"short-":[11],"or":[12,18],"long-range":[13],"dependent":[14],"processes":[15],"finite":[17],"infinite":[19],"variance.":[20],"We":[21],"are":[22,71,87],"concerned":[23],"the":[25,29,69,102,111],"convergence":[26,112],"rate":[27,113],"in":[28,68,82],"strong":[30],"law":[31,42],"of":[32,43,104],"large":[33,44],"numbers":[34,45],"(SLLN).":[35],"Our":[36,85],"main":[37],"result":[38,97],"is":[39,53,61],"Marcinkiewicz\u2013Zygmund":[41],"for":[46,75,114],"$S_{n}(f)=":[47],"\\sum_{i=1}^{n}f(X_{i})$":[48],",":[49],"where":[50],"$\\{X_i\\}_{i\\geq":[51],"1}$":[52],"real":[55],"stationary":[56],"Gaussian":[57],"sequence":[58],"and":[59,107],"$f(\\!\\cdot\\!)$":[60],"measurable":[63],"function.":[64],"Key":[65],"technical":[66],"tools":[67],"proofs":[70],"new":[72,93],"maximal":[73,94],"inequalities":[74],"partial":[76],"sums,":[77],"which":[78],"may":[79],"be":[80],"useful":[81],"other":[83],"problems.":[84],"results":[86],"obtained":[88],"by":[89],"employing":[90],"truncation":[91],"alongside":[92],"inequalities.":[95],"can":[98],"help":[99],"to":[100],"differentiate":[101],"effects":[103],"long":[105],"memory":[106],"heavy":[108],"tails":[109],"on":[110],"limit":[115],"theorems.":[116]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
