{"id":"https://openalex.org/W2996285398","doi":"https://doi.org/10.1080/03610918.2019.1612433","title":"Analytic evaluation of the fractional moments for the quasi-stationary distribution of the Shiryaev martingale on an interval","display_name":"Analytic evaluation of the fractional moments for the quasi-stationary distribution of the Shiryaev martingale on an interval","publication_year":2019,"publication_date":"2019-06-06","ids":{"openalex":"https://openalex.org/W2996285398","doi":"https://doi.org/10.1080/03610918.2019.1612433","mag":"2996285398"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2019.1612433","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1612433","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5085918866","display_name":"Kexuan Li","orcid":"https://orcid.org/0009-0006-0765-0032"},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kexuan Li","raw_affiliation_strings":["Department of Mathematical Sciences, State University of New York (SUNY), Binghamtom, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, State University of New York (SUNY), Binghamtom, NY, USA","institution_ids":["https://openalex.org/I1327163397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016615644","display_name":"Aleksey S. Polunchenko","orcid":"https://orcid.org/0000-0001-8025-4059"},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Aleksey S. Polunchenko","raw_affiliation_strings":["Department of Mathematical Sciences, State University of New York (SUNY), Binghamtom, NY, USA"],"raw_orcid":"https://orcid.org/0000-0001-8025-4059","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, State University of New York (SUNY), Binghamtom, NY, USA","institution_ids":["https://openalex.org/I1327163397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010724031","display_name":"Andrey Pepelyshev","orcid":"https://orcid.org/0000-0001-5634-5559"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB","RU"],"is_corresponding":false,"raw_author_name":"Andrey Pepelyshev","raw_affiliation_strings":["Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia","School of Mathematics, Cardiff University, Cardiff, UK"],"raw_orcid":"https://orcid.org/0000-0001-5634-5559","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"School of Mathematics, Cardiff University, Cardiff, UK","institution_ids":["https://openalex.org/I79510175"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016615644"],"corresponding_institution_ids":["https://openalex.org/I1327163397"],"apc_list":null,"apc_paid":null,"fwci":0.2915,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55493333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"9","first_page":"2705","last_page":"2720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9868000149726868,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9829000234603882,"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/martingale","display_name":"Martingale (probability theory)","score":0.6469944715499878},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5713385343551636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48388370871543884},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.46897897124290466},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3757026791572571},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30619511008262634},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11788782477378845}],"concepts":[{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6469944715499878},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5713385343551636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48388370871543884},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.46897897124290466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3757026791572571},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30619511008262634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11788782477378845},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/03610918.2019.1612433","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1612433","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},{"id":"pmh:oai:http://orca.cardiff.ac.uk:121826","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:http://orca-dev.cardiff.ac.uk:121826","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/121826/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G3052164732","display_name":null,"funder_award_id":"# 304574","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G5538000434","display_name":null,"funder_award_id":"# 17-01-00161","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1533556785","https://openalex.org/W1536128413","https://openalex.org/W1582150714","https://openalex.org/W1648757229","https://openalex.org/W1987617979","https://openalex.org/W1997104875","https://openalex.org/W2004094275","https://openalex.org/W2010042778","https://openalex.org/W2039444550","https://openalex.org/W2046656046","https://openalex.org/W2054097831","https://openalex.org/W2056781959","https://openalex.org/W2057372469","https://openalex.org/W2066406479","https://openalex.org/W2067177556","https://openalex.org/W2093386982","https://openalex.org/W2293209285","https://openalex.org/W2294177012","https://openalex.org/W2313278888","https://openalex.org/W2460673808","https://openalex.org/W2494822901","https://openalex.org/W2593071040","https://openalex.org/W2766426149","https://openalex.org/W2770109889","https://openalex.org/W2963034088","https://openalex.org/W3048065986","https://openalex.org/W3098234070","https://openalex.org/W3105436687","https://openalex.org/W3113221786","https://openalex.org/W3124122391","https://openalex.org/W4205251719","https://openalex.org/W4242317941","https://openalex.org/W4242559281","https://openalex.org/W4250453066"],"related_works":["https://openalex.org/W1922851888","https://openalex.org/W2953059741","https://openalex.org/W3086618278","https://openalex.org/W2951834733","https://openalex.org/W104314157","https://openalex.org/W2406961220","https://openalex.org/W4298231342","https://openalex.org/W2006100586","https://openalex.org/W2963853192","https://openalex.org/W4389982293"],"abstract_inverted_index":{"We":[0,23,57],"consider":[1],"the":[2,6,12,30,40,53,63,71,76,82,89,93,98,102,105],"quasi-stationary":[3,77],"distribution":[4,78,84,96,100],"of":[5,34,55,62,75,81,101,104],"classical":[7],"Shiryaev":[8,106],"diffusion":[9],"restricted":[10],"to":[11],"interval":[13],"[0,A]":[14],"with":[15,44],"absorption":[16],"at":[17],"a":[18,26],"fixed":[19],"A":[20],">":[21],"0.":[22],"derive":[24],"analytically":[25],"closed-form":[27],"formula":[28,41,64],"for":[29,52],"distribution\u2019s":[31],"fractional":[32,73],"moment":[33,74],"an":[35],"arbitrary":[36],"given":[37],"order":[38],"s\u2208R;":[39],"is":[42,97],"consistent":[43],"that":[45,80],"previously":[46],"found":[47],"by":[48,60],"Polunchenko":[49],"and":[50],"Pepelyshev":[51],"case":[54],"s\u2208N.":[56],"also":[58],"show":[59],"virtue":[61],"that,":[65],"if":[66],"s":[67],"<":[68],"1,":[69],"then":[70],"s-th":[72],"becomes":[79],"exponential":[83,95],"(with":[85],"mean":[86],"1/2)":[87],"in":[88],"limit":[90],"as":[91],"A\u2192+\u221e;":[92],"limiting":[94],"stationary":[99],"reciprocal":[103],"diffusion.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}