{"id":"https://openalex.org/W1973665030","doi":"https://doi.org/10.1137/s0036142901390366","title":"Convergence Theory of a Numerical Method for Solving the Chapman--Kolmogorov Equation","display_name":"Convergence Theory of a Numerical Method for Solving the Chapman--Kolmogorov Equation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1973665030","doi":"https://doi.org/10.1137/s0036142901390366","mag":"1973665030"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901390366","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901390366","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5007492415","display_name":"Yuzhi Cai","orcid":"https://orcid.org/0000-0003-3509-9787"},"institutions":[{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yuzhi Cai","raw_affiliation_strings":["#N#University of Surrey#N#"],"affiliations":[{"raw_affiliation_string":"#N#University of Surrey#N#","institution_ids":["https://openalex.org/I28290843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007492415"],"corresponding_institution_ids":["https://openalex.org/I28290843"],"apc_list":null,"apc_paid":null,"fwci":0.3388,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.53742397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":"6","first_page":"2337","last_page":"2351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9505000114440918,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.809624433517456},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6084486246109009},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.603080153465271},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6007493734359741},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.5678425431251526},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5204989314079285},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.47838178277015686},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46286094188690186},{"id":"https://openalex.org/keywords/kolmogorov-equations","display_name":"Kolmogorov equations (Markov jump process)","score":0.419265478849411},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2826985716819763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2448156476020813},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18618494272232056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.809624433517456},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6084486246109009},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.603080153465271},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6007493734359741},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.5678425431251526},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5204989314079285},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.47838178277015686},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46286094188690186},{"id":"https://openalex.org/C59465623","wikidata":"https://www.wikidata.org/wiki/Q6427428","display_name":"Kolmogorov equations (Markov jump process)","level":5,"score":0.419265478849411},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2826985716819763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2448156476020813},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18618494272232056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142901390366","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901390366","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2001343343","https://openalex.org/W2012331797","https://openalex.org/W2048848226","https://openalex.org/W2072208595","https://openalex.org/W2277049871","https://openalex.org/W2314485382","https://openalex.org/W2795454296","https://openalex.org/W2990299855","https://openalex.org/W4299637698"],"related_works":["https://openalex.org/W2150410159","https://openalex.org/W1972271943","https://openalex.org/W3150905897","https://openalex.org/W4327525404","https://openalex.org/W4287185323","https://openalex.org/W2099889858","https://openalex.org/W2171218219","https://openalex.org/W1520183331","https://openalex.org/W2168175994","https://openalex.org/W2167818257"],"abstract_inverted_index":{"A":[0,18],"convergence":[1],"theory":[2,41],"has":[3,42],"been":[4,43],"established":[5],"for":[6,11,22],"a":[7],"new":[8],"numerical":[9],"method":[10],"solving":[12],"the":[13],"Chapman--Kolmogorov":[14],"equation":[15],"[Y.":[16],"Cai,":[17],"Numerical":[19],"Forecasting":[20],"Procedure":[21],"Nonlinear":[23],"Autoregressive":[24],"Time":[25],"Series":[26],"Model,":[27],"manuscript,":[28],"Department":[29],"of":[30,35,48],"Mathematics":[31],"and":[32,69],"Statistics,":[33],"University":[34],"Surrey,":[36,37],"UK,":[38],"2001].":[39],"The":[40],"applied":[44],"to":[45,55],"many":[46],"types":[47],"nonlinear":[49],"time":[50],"series":[51],"models":[52],"in":[53],"order":[54],"obtain":[56],"m-step":[57],"ahead":[58],"predictive":[59,63,67,70],"probability":[60],"density":[61],"function,":[62,66],"cumulative":[64],"distribution":[65],"mean,":[68],"variance.":[71]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}