{"id":"https://openalex.org/W2950139667","doi":"https://doi.org/10.1017/s002190020001161x","title":"Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps","display_name":"Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps","publication_year":2014,"publication_date":"2014-09-01","ids":{"openalex":"https://openalex.org/W2950139667","doi":"https://doi.org/10.1017/s002190020001161x","mag":"2950139667"},"language":"en","primary_location":{"id":"doi:10.1017/s002190020001161x","is_oa":false,"landing_page_url":"http://doi.org/10.1017/s002190020001161x","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/A5103238499","display_name":"Lingjiong Zhu","orcid":"https://orcid.org/0000-0001-7595-160X"},"institutions":[{"id":"https://openalex.org/I15196421","display_name":"University of Applied Sciences and Arts of Southern Switzerland","ror":"https://ror.org/05ep8g269","country_code":"CH","type":"education","lineage":["https://openalex.org/I15196421"]},{"id":"https://openalex.org/I4210102264","display_name":"Shandong University of Political Science and Law","ror":"https://ror.org/01b2j5886","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210102264"]},{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]}],"countries":["CH","CN","FR"],"is_corresponding":true,"raw_author_name":"Lingjiong Zhu","raw_affiliation_strings":["New York University<sup>**</sup>"],"affiliations":[{"raw_affiliation_string":"New York University<sup>**</sup>","institution_ids":["https://openalex.org/I15196421","https://openalex.org/I4210102264","https://openalex.org/I102475099"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103238499"],"corresponding_institution_ids":["https://openalex.org/I102475099","https://openalex.org/I15196421","https://openalex.org/I4210102264"],"apc_list":null,"apc_paid":null,"fwci":4.6329,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.94865835,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"03","first_page":"699","last_page":"712"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.972599983215332,"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":0.9704999923706055,"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/mathematics","display_name":"Mathematics","score":0.7178499698638916},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6544123888015747},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.6384873390197754},{"id":"https://openalex.org/keywords/cox\u2013ingersoll\u2013ross-model","display_name":"Cox\u2013Ingersoll\u2013Ross model","score":0.62259441614151},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6207664012908936},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5217828750610352},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.5192187428474426},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.46939414739608765},{"id":"https://openalex.org/keywords/cox-process","display_name":"Cox process","score":0.46534690260887146},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.46111157536506653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45737767219543457},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4529139995574951},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.437260240316391},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.39600658416748047},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.38246461749076843},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3788061738014221},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3225124478340149},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28670352697372437},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.18858081102371216},{"id":"https://openalex.org/keywords/poisson-process","display_name":"Poisson process","score":0.15444475412368774},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1512693464756012},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08766451478004456},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08331862092018127},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.0677725076675415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7178499698638916},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6544123888015747},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.6384873390197754},{"id":"https://openalex.org/C151205565","wikidata":"https://www.wikidata.org/wiki/Q4385634","display_name":"Cox\u2013Ingersoll\u2013Ross model","level":3,"score":0.62259441614151},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6207664012908936},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5217828750610352},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.5192187428474426},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.46939414739608765},{"id":"https://openalex.org/C155051063","wikidata":"https://www.wikidata.org/wiki/Q1290919","display_name":"Cox process","level":4,"score":0.46534690260887146},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.46111157536506653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45737767219543457},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4529139995574951},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.437260240316391},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.39600658416748047},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38246461749076843},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3788061738014221},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3225124478340149},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28670352697372437},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.18858081102371216},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.15444475412368774},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1512693464756012},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08766451478004456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08331862092018127},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0677725076675415},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C175025494","wikidata":"https://www.wikidata.org/wiki/Q179179","display_name":"Interest rate","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s002190020001161x","is_oa":false,"landing_page_url":"http://doi.org/10.1017/s002190020001161x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1539015357","https://openalex.org/W1752898370","https://openalex.org/W1979276750","https://openalex.org/W2035003768","https://openalex.org/W2060940929","https://openalex.org/W2064978316","https://openalex.org/W2069849731","https://openalex.org/W2075321234","https://openalex.org/W2088067727","https://openalex.org/W2165789588","https://openalex.org/W2166822347","https://openalex.org/W2311961928","https://openalex.org/W2328875713","https://openalex.org/W2329986772","https://openalex.org/W2949407832","https://openalex.org/W2951479065","https://openalex.org/W2953310116","https://openalex.org/W2963002972","https://openalex.org/W3021444882","https://openalex.org/W3121146574","https://openalex.org/W4211159534"],"related_works":["https://openalex.org/W4223985063","https://openalex.org/W2952190099","https://openalex.org/W1964430252","https://openalex.org/W2769873724","https://openalex.org/W4313398236","https://openalex.org/W1993881909","https://openalex.org/W2606420300","https://openalex.org/W2950139667","https://openalex.org/W2020958959","https://openalex.org/W4311071379"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"propose":[4],"a":[5,10,21,40],"stochastic":[6],"process,":[7],"which":[8],"is":[9,39],"Cox-Ingersoll-Ross":[11,26],"process":[12,27,32],"with":[13,33],"Hawkes":[14,31],"jumps.":[15],"It":[16],"can":[17],"be":[18],"seen":[19],"as":[20],"generalization":[22],"of":[23,43,58],"the":[24,29,44,56],"classical":[25,30],"and":[28,52,64],"exponential":[34],"exciting":[35],"function.":[36],"Our":[37],"model":[38],"special":[41],"case":[42],"affine":[45],"point":[46],"processes.":[47],"We":[48],"obtain":[49],"Laplace":[50],"transforms":[51],"limit":[53,62],"theorems,":[54,63],"including":[55],"law":[57],"large":[59,65],"numbers,":[60],"central":[61],"deviations.":[66]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
