{"id":"https://openalex.org/W1997425561","doi":"https://doi.org/10.1155/2007/83852","title":"Long-Range Dependence in a Cox Process Directed by a Markov Renewal Process","display_name":"Long-Range Dependence in a Cox Process Directed by a Markov Renewal Process","publication_year":2007,"publication_date":"2007-11-22","ids":{"openalex":"https://openalex.org/W1997425561","doi":"https://doi.org/10.1155/2007/83852","mag":"1997425561"},"language":"lv","primary_location":{"id":"doi:10.1155/2007/83852","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/83852","pdf_url":"https://downloads.hindawi.com/archive/2007/083852.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Mathematics and Decision Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2007/083852.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026649461","display_name":"D. J. Daley","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"D. J. Daley","raw_affiliation_strings":["Centre for Mathematics and its Applications, The Australian National University, ACT 0200"],"affiliations":[{"raw_affiliation_string":"Centre for Mathematics and its Applications, The Australian National University, ACT 0200","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030111068","display_name":"Tomasz Rolski","orcid":"https://orcid.org/0000-0002-9835-9681"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"T. Rolski","raw_affiliation_strings":["Mathematical Institute, University of Wroc\u0142aw, pl. Grunwaldzki 2/4, Wroc\u0142aw 50384"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Wroc\u0142aw, pl. Grunwaldzki 2/4, Wroc\u0142aw 50384","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069822730","display_name":"Rein Vesilo","orcid":"https://orcid.org/0000-0002-5957-1938"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"R. Vesilo","raw_affiliation_strings":["Department of Electronics, Macquarie University, North Ryde, NSW 2109"],"affiliations":[{"raw_affiliation_string":"Department of Electronics, Macquarie University, North Ryde, NSW 2109","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026649461"],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":null,"apc_paid":null,"fwci":0.4475,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57920051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2007","issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9911999702453613,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9911999702453613,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9732999801635742,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9714999794960022,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/algorithm","display_name":"Algorithm","score":0.3728218078613281},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21429723501205444}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3728218078613281},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21429723501205444}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2007/83852","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/83852","pdf_url":"https://downloads.hindawi.com/archive/2007/083852.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Mathematics and Decision Sciences","raw_type":"journal-article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/34329","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/34329","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"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 Mathematics and Decision Sciences","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1155/2007/83852","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/83852","pdf_url":"https://downloads.hindawi.com/archive/2007/083852.pdf","source":{"id":"https://openalex.org/S187318915","display_name":"Journal of Applied Mathematics and Decision Sciences","issn_l":"1173-9126","issn":["1173-9126","1532-7612"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Mathematics and Decision Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G317368514","display_name":null,"funder_award_id":"MTKD-CT-2004-13389","funder_id":"https://openalex.org/F4320325012","funder_display_name":"Uniwersytet Wroc\u0142awski"}],"funders":[{"id":"https://openalex.org/F4320325012","display_name":"Uniwersytet Wroc\u0142awski","ror":"https://ror.org/00yae6e25"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997425561.pdf","grobid_xml":"https://content.openalex.org/works/W1997425561.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2014420092","https://openalex.org/W2329734432","https://openalex.org/W3026026050"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"A":[0],"Cox":[1],"process":[2,85,103,132],"<mml:math":[3,12,18,26,37,48,52,66,73,78,92,96,105,126,137,152,165,170,177,196,203,214,222,227,232,235,240,249,255,261],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,13,19,27,29,38,49,53,67,74,79,93,97,106,127,138,153,166,171,178,197,204,215,223,228,233,236,241,250,256,262],"id=\"E1\"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>Cox</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>":[5],"directed":[6],"by":[7,24,58,120],"a":[8,59,100,146],"stationary":[9,81,101],"random":[10,46,109],"measure":[11,47,110],"id=\"E2\"><mml:mi>\u03be</mml:mi></mml:math>":[14],"has":[15,140,181,206],"second":[16,142,183],"moment":[17,184],"id=\"E3\"><mml:mrow><mml:mtext>var</mml:mtext><mml:mtext>":[20],"</mml:mtext><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>Cox</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mtext>E</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>\u03be</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mtext>var</mml:mtext><mml:mtext>":[21],"</mml:mtext><mml:mi>\u03be</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math>,":[22],"where":[23,248],"stationarity":[25],"id=\"E4\"><mml:mtext>E</mml:mtext><mml:mo>(</mml:mo><mml:mi>\u03be</mml:mi><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>]</mml:mo><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mtext>const</mml:mtext><mml:mo>.</mml:mo><mml:mo>)</mml:mo><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:math><mml:math":[28],"id=\"E5\"><mml:mtext>E</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mtext>Cox</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>]</mml:mo><mml:mo>)</mml:mo></mml:math>,":[30],"so":[31],"long-range":[32],"dependence":[33],"(LRD)":[34],"properties":[35,43],"of":[36,44,76,130,221],"id=\"E6\"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>Cox</mml:mtext></mml:mrow></mml:msub></mml:math>":[39],"coincide":[40],"with":[41,173],"LRD":[42,112],"the":[45,70,108,131,207,212,219],"id=\"E7\"><mml:mi>\u03be</mml:mi></mml:math>.":[50],"When":[51],"id=\"E8\"><mml:mi>\u03be</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle":[54],"displaystyle=\"true\"><mml:mrow><mml:msub><mml:mo>\u222b</mml:mo><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:msub><mml:mi>\u03bd</mml:mi><mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mstyle><mml:mtext>d</mml:mtext><mml:mi>u</mml:mi></mml:math>":[55],"is":[56,99,111,155,157,192,199],"determined":[57],"density":[60],"that":[61,158,189,217],"depends":[62],"on":[63,104],"rate":[64],"parameters":[65],"id=\"E9\"><mml:msub><mml:mi>\u03bd</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>\ud835\udd4f</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>":[68],"and":[69,114,148],"current":[71],"state":[72,90,136,169],"id=\"E10\"><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>\u22c5</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math>":[75],"an":[77],"id=\"E11\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>-valued":[80],"irreducible":[82],"Markov":[83],"renewal":[84],"(MRP)":[86],"for":[87,133,144,230],"some":[88],"countable":[89],"space":[91],"id=\"E12\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>":[94],"(so":[95],"id=\"E13\"><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[98],"semi-Markov":[102],"id=\"E14\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>),":[107],"if":[113,116],"only":[115],"each":[117],"(and":[118],"then":[119],"irreducibility,":[121],"every)":[122],"generic":[123,162],"return":[124],"time":[125,164],"id=\"E15\"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>\u2208</mml:mo><mml:mi":[128],"mathvariant=\"double-struck\">X</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>":[129],"entries":[134],"to":[135],"id=\"E16\"><mml:mi>j</mml:mi></mml:math>":[139],"infinite":[141,182],"moment,":[143],"which":[145],"necessary":[147,194],"sufficient":[149],"condition":[150,191],"when":[151,195],"id=\"E17\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>":[154],"finite":[156,231],"at":[159],"least":[160],"one":[161],"holding":[163],"id=\"E18\"><mml:msub><mml:mi>X</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math>":[167],"in":[168],"id=\"E19\"><mml:mi>j</mml:mi></mml:math>,":[172],"distribution":[174],"function":[175],"(DF)\\":[176],"id=\"E20\"><mml:msub><mml:mi>H</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math>,":[179],"say,":[180],"(a":[185],"simple":[186],"example":[187],"shows":[188],"this":[190],"not":[193],"id=\"E21\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>":[198],"countably":[200],"infinite).":[201],"Then,":[202],"id=\"E22\"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>Cox</mml:mtext></mml:mrow></mml:msub></mml:math>":[205],"same":[208],"Hurst":[209],"index":[210],"as":[211,226],"MRP":[213],"id=\"E23\"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>MRP</mml:mtext></mml:mrow></mml:msub></mml:math>":[216],"counts":[218],"jumps":[220],"id=\"E24\"><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>\u22c5</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math>,":[224],"while":[225],"id=\"E25\"><mml:mi>t</mml:mi><mml:mo>\u2192</mml:mo><mml:mi>\u221e</mml:mi></mml:math>,":[229],"id=\"E26\"><mml:mi>\ud835\udd4f</mml:mi></mml:math>,":[234],"id=\"E27\"><mml:mtext>var</mml:mtext><mml:mtext>":[237],"</mml:mtext><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>MRP</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>\u223c</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mi>\u03bb</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mstyle":[238],"displaystyle=\"true\"><mml:mrow><mml:msubsup><mml:mo>\u222b</mml:mo><mml:mn>0</mml:mn><mml:mi>t</mml:mi></mml:msubsup><mml:mrow><mml:mi>\ud835\udca2</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mstyle><mml:mtext>d</mml:mtext><mml:mi>u</mml:mi></mml:math>,":[239],"id=\"E28\"><mml:mtext>var</mml:mtext><mml:mtext>":[242],"</mml:mtext><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mtext>Cox</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>\u223c</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mstyle":[243],"displaystyle=\"true\"><mml:mrow><mml:msubsup><mml:mo>\u222b</mml:mo><mml:mn>0</mml:mn><mml:mi>t</mml:mi></mml:msubsup><mml:mrow><mml:mstyle":[244],"displaystyle=\"true\"><mml:munder><mml:mo>\u2211</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>\ud835\udd4f</mml:mi></mml:mrow></mml:munder><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>\u03bd</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>\u2212</mml:mo><mml:mover":[245],"accent=\"true\"><mml:mi>\u03bd</mml:mi><mml:mo":[246,252],"stretchy=\"true\">\u00af</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:mrow></mml:mrow></mml:mstyle><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>\u03d6</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>\u210b</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>du</mml:mtext></mml:math>,":[247],"id=\"E29\"><mml:mover":[251],"stretchy=\"true\">\u00af</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mstyle":[253],"displaystyle=\"true\"><mml:msub><mml:mo>\u2211</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:msub><mml:mi>\u03d6</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>\u03bd</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>E</mml:mtext></mml:mrow></mml:mstyle><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>\u03be</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>,":[254],"id=\"E30\"><mml:msub><mml:mi>\u03d6</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>Pr</mml:mtext><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>\u03bb</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mstyle":[257],"displaystyle=\"true\"><mml:msub><mml:mo>\u2211</mml:mo><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:msub><mml:mover":[258],"accent=\"true\"><mml:mi>p</mml:mi><mml:mo":[259],"stretchy=\"true\">\u02c7</mml:mo></mml:mover><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi>\u03bc</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:math>,":[260],"id=\"E31\"><mml:msub><mml:mi>\u03bc</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>E</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>j<":[263]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}