{"id":"https://openalex.org/W4416335853","doi":"https://doi.org/10.1017/jpr.2025.10047","title":"Scaling limits for supercritical nearly unstable Hawkes processes","display_name":"Scaling limits for supercritical nearly unstable Hawkes processes","publication_year":2025,"publication_date":"2025-11-19","ids":{"openalex":"https://openalex.org/W4416335853","doi":"https://doi.org/10.1017/jpr.2025.10047"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.10047","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10047","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1017/jpr.2025.10047","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100348056","display_name":"Chenguang Liu","orcid":"https://orcid.org/0009-0002-3635-257X"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Chenguang Liu","raw_affiliation_strings":["TU Delft"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Delft","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058528886","display_name":"Liping Xu","orcid":"https://orcid.org/0000-0002-2683-7963"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liping Xu","raw_affiliation_strings":["Beihang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100601643","display_name":"An Zhang","orcid":"https://orcid.org/0000-0002-9338-6250"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"An Zhang","raw_affiliation_strings":["Beihang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058528886","https://openalex.org/A5100348056","https://openalex.org/A5100601643"],"corresponding_institution_ids":["https://openalex.org/I82880672","https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44568182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"2","first_page":"607","last_page":"622"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9625999927520752,"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":0.9625999927520752,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.011599999852478504,"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"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/scaling","display_name":"Scaling","score":0.791700005531311},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5318999886512756},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5090000033378601},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4864000082015991},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.45350000262260437},{"id":"https://openalex.org/keywords/scaling-law","display_name":"Scaling law","score":0.44279998540878296},{"id":"https://openalex.org/keywords/supercritical-fluid","display_name":"Supercritical fluid","score":0.4381999969482422}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.791700005531311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7390000224113464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.703499972820282},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.45350000262260437},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.44279998540878296},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39959999918937683},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2775999903678894},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2637999951839447}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/jpr.2025.10047","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10047","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/jpr.2025.10047","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10047","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1539015357","https://openalex.org/W1752898370","https://openalex.org/W1879773776","https://openalex.org/W1950412443","https://openalex.org/W1979276750","https://openalex.org/W2014601298","https://openalex.org/W2042034885","https://openalex.org/W2052197092","https://openalex.org/W2057139325","https://openalex.org/W2060940929","https://openalex.org/W2069849731","https://openalex.org/W2075321234","https://openalex.org/W2079544355","https://openalex.org/W2088067727","https://openalex.org/W2154841817","https://openalex.org/W2154952087","https://openalex.org/W2328875713","https://openalex.org/W2594472342","https://openalex.org/W2776498136","https://openalex.org/W2795931350","https://openalex.org/W2964026625","https://openalex.org/W2964255676","https://openalex.org/W3016631000","https://openalex.org/W3021444882","https://openalex.org/W3110394477","https://openalex.org/W3121115911","https://openalex.org/W3201203679","https://openalex.org/W4236324996","https://openalex.org/W4293092461","https://openalex.org/W4399593501","https://openalex.org/W4405544014"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,47],"investigate":[2],"the":[3,50,54,58,142,145,183,200],"asymptotic":[4],"behavior":[5,56],"of":[6,57,71,144,147,157],"nearly":[7],"unstable":[8],"Hawkes":[9,148],"processes":[10,59,149],"whose":[11],"regression":[12],"kernel":[13],"has":[14],"upper":[15,76,85,92,95,161],"L":[16],"Superscript":[17,88,94],"1":[18,37,41,80,158],"<mml:math":[19,98,164],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"":[20,99,165],"xmlns:mnf=\"http://cambridge.org/core/manifest\"":[21,100,166],"xmlns:cup=\"http://contentservices.cambridge.org\"":[22,101,167],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[23,102,168],"xmlns:m=\"http://cambridge.org/core/metadata\"":[24,103,169],"xmlns:core=\"http://cambridge.org/core\"":[25,104,170],"xmlns:c=\"http://cambridge.org/core/content\">":[26,105,171],"<mml:msup>":[27,123,176],"<mml:mi>L</mml:mi>":[28],"<mml:mn>1</mml:mn>":[29,114,172],"</mml:msup>":[30,137,179],"</mml:math>":[31,139,180],"$L^1$":[32],"norm":[33],"strictly":[34],"greater":[35],"than":[36],"and":[38,63,206],"close":[39],"to":[40,45,188,198],"as":[42,60],"time":[43],"goes":[44],"infinity.":[46],"find":[48],"that":[49],"scaling":[51,55],"size":[52],"determines":[53],"in":[61,186,204,208],"Jaisson":[62],"Rosenbaum":[64],"(2015).":[65],"Specifically,":[66],"after":[67],"a":[68,74],"suitable":[69],"rescale":[70],"left":[72],"parenthesis":[73,82],"Subscript":[75,91],"T":[77,86,93,96,162],"Baseline":[78],"minus":[79],"right":[81],"divided":[83,159],"by":[84,160],"e":[87],"b":[89],"Super":[90],"x":[97],"<mml:mo":[106,116],"stretchy=\"false\">(</mml:mo>":[107],"<mml:mrow>":[108,118,121,124,125,129,173],"<mml:msub>":[109,130],"<mml:mi>a</mml:mi>":[110],"<mml:mi>T</mml:mi>":[111,122,132,134,177],"</mml:msub>":[112,133],"<mml:mo>\u2212</mml:mo>":[113],"</mml:mrow>":[115,120,127,128,136,138,175],"stretchy=\"false\">)</mml:mo>":[117],"<mml:mo>/</mml:mo>":[119,174],"<mml:mtext>e</mml:mtext>":[126],"<mml:mi>b</mml:mi>":[131],"<mml:mi>x</mml:mi>":[135],"$({a_T-1})/{T{\\textrm{e}}^{b_TTx}}$":[140],",":[141,182],"limit":[143],"sequence":[146,184],"is":[150],"deterministic.":[151],"Also,":[152],"with":[153],"another":[154],"appropriate":[155],"rescaling":[156],"squared":[163],"<mml:mn>2</mml:mn>":[178],"$1/T^2$":[181],"converges":[185],"law":[187],"an":[189],"integrated":[190],"Cox\u2013Ingersoll\u2013Ross-like":[191],"process.":[192],"This":[193],"theoretical":[194],"result":[195],"may":[196],"apply":[197],"model":[199],"recent":[201],"COVID-19":[202],"outbreak":[203],"epidemiology":[205],"phenomena":[207],"social":[209],"networks.":[210]},"counts_by_year":[],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2025-11-19T00:00:00"}
