{"id":"https://openalex.org/W7130702195","doi":"https://doi.org/10.1007/s11134-026-09974-5","title":"Second order properties of thinned counts in finite birth\u2013death processes","display_name":"Second order properties of thinned counts in finite birth\u2013death processes","publication_year":2026,"publication_date":"2026-02-20","ids":{"openalex":"https://openalex.org/W7130702195","doi":"https://doi.org/10.1007/s11134-026-09974-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11134-026-09974-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-026-09974-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-026-09974-5.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","0340-4384","1572-9443"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11134-026-09974-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026649461","display_name":"D. J. Daley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daryl. J. Daley","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070445330","display_name":"Yoni Nazarathy","orcid":"https://orcid.org/0000-0003-3071-8462"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Yoni Nazarathy","raw_affiliation_strings":["School of Mathematics and Physics, The University of Queensland, Queensland, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, The University of Queensland, Queensland, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126460923","display_name":"Jiesen Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Jiesen Wang","raw_affiliation_strings":["Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-2709-6586","affiliations":[{"raw_affiliation_string":"Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5126460923"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13533183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"110","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9470999836921692,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9470999836921692,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.019500000402331352,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0032999999821186066,"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/birth\u2013death-process","display_name":"Birth\u2013death process","score":0.6715999841690063},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.6380000114440918},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.548799991607666},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5156999826431274},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5115000009536743},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.4607999920845032},{"id":"https://openalex.org/keywords/bernoulli-process","display_name":"Bernoulli process","score":0.45660001039505005},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45570001006126404},{"id":"https://openalex.org/keywords/bernoulli-trial","display_name":"Bernoulli trial","score":0.45080000162124634},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.44339999556541443}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6779000163078308},{"id":"https://openalex.org/C65990518","wikidata":"https://www.wikidata.org/wiki/Q1456275","display_name":"Birth\u2013death process","level":3,"score":0.6715999841690063},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.548799991607666},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5115000009536743},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5112000107765198},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.4607999920845032},{"id":"https://openalex.org/C23990920","wikidata":"https://www.wikidata.org/wiki/Q518831","display_name":"Bernoulli process","level":3,"score":0.45660001039505005},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C46802686","wikidata":"https://www.wikidata.org/wiki/Q1077800","display_name":"Bernoulli trial","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C2983497884","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite state","level":3,"score":0.41929998993873596},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C49698424","wikidata":"https://www.wikidata.org/wiki/Q1989192","display_name":"Law of total probability","level":4,"score":0.3239000141620636},{"id":"https://openalex.org/C177255742","wikidata":"https://www.wikidata.org/wiki/Q4109953","display_name":"Branching process","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C2962069","wikidata":"https://www.wikidata.org/wiki/Q5462733","display_name":"Fluid queue","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C15964574","wikidata":"https://www.wikidata.org/wiki/Q7295534","display_name":"Rate function","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C2781104640","wikidata":"https://www.wikidata.org/wiki/Q11827313","display_name":"Counting process","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C971699","wikidata":"https://www.wikidata.org/wiki/Q1132714","display_name":"Delta method","level":3,"score":0.2754000127315521},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26429998874664307},{"id":"https://openalex.org/C116930293","wikidata":"https://www.wikidata.org/wiki/Q5265717","display_name":"Deterministic system (philosophy)","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11134-026-09974-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-026-09974-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-026-09974-5.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","0340-4384","1572-9443"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11134-026-09974-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-026-09974-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11134-026-09974-5.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","0340-4384","1572-9443"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5241223922","display_name":null,"funder_award_id":"101034253","funder_id":"https://openalex.org/F4320338438","funder_display_name":"HORIZON EUROPE Marie Sklodowska-Curie Actions"},{"id":"https://openalex.org/G565383568","display_name":null,"funder_award_id":"024-002-003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8639291584","display_name":"NETCO-PD: 14 experienced researchers in network science for Europe","funder_award_id":"101034253","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320338438","display_name":"HORIZON EUROPE Marie Sklodowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W7130702195.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W633278723","https://openalex.org/W2004762667","https://openalex.org/W2024786776","https://openalex.org/W2054817414","https://openalex.org/W2056645762","https://openalex.org/W2075520098","https://openalex.org/W2103154048","https://openalex.org/W2108742061","https://openalex.org/W2147218457","https://openalex.org/W2781700023","https://openalex.org/W3165298582","https://openalex.org/W4292641442","https://openalex.org/W4313704025","https://openalex.org/W4390108477"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1],"paper":[2],"studies":[3],"the":[4,30,38,51,54,78,88,91,95,104,109,115],"counting":[5],"process":[6,18,31,58],"arising":[7],"as":[8,87],"a":[9,16,20,25,48,66,75],"subset":[10],"of":[11,40,50,53,82,90,106,108],"births":[12],"and":[13,56,59,94,122],"deaths":[14],"in":[15],"birth\u2013death":[17],"on":[19,37,62],"finite":[21],"state":[22,52,118],"space.":[23],"Whenever":[24],"birth":[26,55,67],"or":[27,34,68],"death":[28,57,69],"occurs,":[29],"is":[32,47,65,120],"incremented":[33],"not":[35],"depending":[36],"outcome":[39],"an":[41],"independent":[42],"Bernoulli":[43],"experiment":[44],"whose":[45],"probability":[46],"function":[49],"also":[60,85],"depends":[61],"whether":[63],"it":[64],"that":[70],"has":[71],"occurred.":[72],"We":[73],"establish":[74],"formula":[76,113],"for":[77,114],"asymptotic":[79,92,96],"variance":[80,93],"rate":[81],"this":[83],"process,":[84],"presented":[86],"ratio":[89],"mean.":[97],"Several":[98],"examples":[99],"including":[100],"queueing":[101],"models":[102],"illustrate":[103],"scope":[105],"applicability":[107],"results.":[110],"An":[111],"analogous":[112],"countably":[116],"infinite":[117],"space":[119],"conjectured":[121],"tested.":[123]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2026-02-21T00:00:00"}
