{"id":"https://openalex.org/W1997059569","doi":"https://doi.org/10.1515/156939603322601932","title":"A Quasi Monte Carlo Approach to Piecewise Linear Markov Approximations of Markov Operators","display_name":"A Quasi Monte Carlo Approach to Piecewise Linear Markov Approximations of Markov Operators","publication_year":2003,"publication_date":"2003-12-01","ids":{"openalex":"https://openalex.org/W1997059569","doi":"https://doi.org/10.1515/156939603322601932","mag":"1997059569"},"language":"en","primary_location":{"id":"doi:10.1515/156939603322601932","is_oa":true,"landing_page_url":"http://doi.org/10.1515/156939603322601932","pdf_url":"http://www.degruyter.com/downloadpdf/j/mcma.2003.9.issue-4/156939603322601932/156939603322601932.xml","source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Monte Carlo Methods and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://www.degruyter.com/downloadpdf/j/mcma.2003.9.issue-4/156939603322601932/156939603322601932.xml","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021040219","display_name":"Jiu Ding","orcid":"https://orcid.org/0000-0003-1360-9432"},"institutions":[{"id":"https://openalex.org/I44854399","display_name":"University of Southern Mississippi","ror":"https://ror.org/0270vfa57","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I44854399"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiu Ding","raw_affiliation_strings":["1. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA","institution_ids":["https://openalex.org/I44854399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072702653","display_name":"Dong Mao","orcid":"https://orcid.org/0000-0002-5744-6316"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong Mao","raw_affiliation_strings":["2. Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2. Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113202217","display_name":"Aihui Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aihui Zhou","raw_affiliation_strings":["3. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"3. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12645529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"4","first_page":"295","last_page":"309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9933000206947327,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9933000206947327,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9933000206947327,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9765999913215637,"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/markov-chain","display_name":"Markov chain","score":0.6146831512451172},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5666905045509338},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.5572115182876587},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.5441994071006775},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5041340589523315},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5000889301300049},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4863319993019104},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4654209315776825},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.4472997188568115},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4197283387184143},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4047158360481262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3857429325580597},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37570422887802124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12293636798858643},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08494111895561218},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0662958025932312}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6146831512451172},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5666905045509338},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.5572115182876587},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.5441994071006775},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5041340589523315},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5000889301300049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4863319993019104},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4654209315776825},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.4472997188568115},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4197283387184143},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4047158360481262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3857429325580597},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37570422887802124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12293636798858643},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08494111895561218},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0662958025932312}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/156939603322601932","is_oa":true,"landing_page_url":"http://doi.org/10.1515/156939603322601932","pdf_url":"http://www.degruyter.com/downloadpdf/j/mcma.2003.9.issue-4/156939603322601932/156939603322601932.xml","source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Monte Carlo Methods and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:bpj:mcmeap:v:9:y:2003:i:4:p:295-309:n:1","is_oa":false,"landing_page_url":"https://doi.org/10.1515/156939603322601932","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":{"id":"doi:10.1515/156939603322601932","is_oa":true,"landing_page_url":"http://doi.org/10.1515/156939603322601932","pdf_url":"http://www.degruyter.com/downloadpdf/j/mcma.2003.9.issue-4/156939603322601932/156939603322601932.xml","source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Monte Carlo Methods and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1489458628","https://openalex.org/W1503719492","https://openalex.org/W1533006072","https://openalex.org/W1534163925","https://openalex.org/W1553236419","https://openalex.org/W1592472301","https://openalex.org/W1969918410","https://openalex.org/W1997815317","https://openalex.org/W2005680619","https://openalex.org/W2006065933","https://openalex.org/W2043016630","https://openalex.org/W2055168065","https://openalex.org/W2055729437","https://openalex.org/W2059713984","https://openalex.org/W2073154039","https://openalex.org/W2080600582","https://openalex.org/W2482944896"],"related_works":["https://openalex.org/W2130519334","https://openalex.org/W1985664346","https://openalex.org/W2382132287","https://openalex.org/W1493775604","https://openalex.org/W2363310627","https://openalex.org/W2353444478","https://openalex.org/W4240129243","https://openalex.org/W1504767525","https://openalex.org/W4360597163","https://openalex.org/W3216708645"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"address":[4],"the":[5,17,40],"computational":[6],"issue":[7],"of":[8,20,33],"approximating":[9],"Markov":[10,36,41],"operators":[11],"which":[12],"are":[13],"widely":[14],"used":[15],"in":[16],"stochastic":[18],"study":[19],"chaotic":[21],"dynamical":[22],"systems.":[23],"We":[24],"will":[25],"concentrate":[26],"on":[27],"a":[28],"quasi":[29],"Monte":[30],"Carlo":[31],"implementation":[32],"piecewise":[34],"linear":[35],"approximations":[37],"that":[38],"preserve":[39],"structure.":[42]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}