{"id":"https://openalex.org/W2149690228","doi":"https://doi.org/10.1142/s021812740902297x","title":"INVARIANT MEASURES FOR HIGHER DIMENSIONAL MARKOV SWITCHING POSITION DEPENDENT RANDOM MAPS","display_name":"INVARIANT MEASURES FOR HIGHER DIMENSIONAL MARKOV SWITCHING POSITION DEPENDENT RANDOM MAPS","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2149690228","doi":"https://doi.org/10.1142/s021812740902297x","mag":"2149690228"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740902297x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902297x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5029610015","display_name":"Md. Shafiqul Islam","orcid":"https://orcid.org/0000-0002-5389-2634"},"institutions":[{"id":"https://openalex.org/I22188714","display_name":"University of Prince Edward Island","ror":"https://ror.org/02xh9x144","country_code":"CA","type":"education","lineage":["https://openalex.org/I22188714"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"MD SHAFIQUL ISLAM","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Ave, Charlottetown, PE, C1A 4P3, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Ave, Charlottetown, PE, C1A 4P3, Canada","institution_ids":["https://openalex.org/I22188714"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029610015"],"corresponding_institution_ids":["https://openalex.org/I22188714"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19202562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"01","first_page":"409","last_page":"417"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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":0.9997000098228455,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9915000200271606,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9613000154495239,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.7478803396224976},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7409065961837769},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5885159969329834},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5849249362945557},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5194477438926697},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.45319047570228577},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4525347352027893},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4454084634780884},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.43321841955184937},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.42895835638046265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3792508840560913},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35210973024368286},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3450673520565033},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.32295167446136475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2780616879463196},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.131942480802536},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.09487631916999817}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7478803396224976},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7409065961837769},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5885159969329834},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5849249362945557},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5194477438926697},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.45319047570228577},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4525347352027893},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4454084634780884},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.43321841955184937},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.42895835638046265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3792508840560913},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35210973024368286},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3450673520565033},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.32295167446136475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2780616879463196},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.131942480802536},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.09487631916999817},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812740902297x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902297x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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":21,"referenced_works":["https://openalex.org/W837642393","https://openalex.org/W939789283","https://openalex.org/W1489458628","https://openalex.org/W1969665421","https://openalex.org/W1978718596","https://openalex.org/W1987271446","https://openalex.org/W1990522469","https://openalex.org/W2022373315","https://openalex.org/W2022841413","https://openalex.org/W2033815552","https://openalex.org/W2037938678","https://openalex.org/W2050657567","https://openalex.org/W2086099418","https://openalex.org/W2088964933","https://openalex.org/W2155870008","https://openalex.org/W2336476235","https://openalex.org/W2339378878","https://openalex.org/W2746397983","https://openalex.org/W4235476465","https://openalex.org/W4247385211","https://openalex.org/W4254718130"],"related_works":["https://openalex.org/W2027903142","https://openalex.org/W2989366387","https://openalex.org/W3104611551","https://openalex.org/W2735859191","https://openalex.org/W2592341669","https://openalex.org/W2794873331","https://openalex.org/W2376290921","https://openalex.org/W4252142810","https://openalex.org/W2387462590","https://openalex.org/W50519898"],"abstract_inverted_index":{"A":[0],"higher":[1,20,60],"dimensional":[2,61],"Markov":[3,62],"switching":[4,17,63],"position":[5,64],"dependent":[6,65],"random":[7,11,66],"map":[8,12],"is":[9,70],"a":[10,29,57,71],"where":[13],"the":[14,26,33,50,74],"probabilities":[15],"of":[16,28,35,40,52,59,73],"from":[18],"one":[19],"dimension":[21],"transformation":[22],"to":[23],"another":[24],"are":[25,38],"entries":[27,34],"stochastic":[30,36],"matrix":[31,37],"and":[32],"functions":[39],"positions.":[41],"In":[42],"this":[43],"note,":[44],"we":[45],"prove":[46],"sufficient":[47],"conditions":[48],"for":[49,56],"existence":[51],"absolutely":[53],"continuous":[54],"measures":[55],"class":[58],"maps.":[67],"Our":[68],"result":[69,75],"generalization":[72],"in":[76],"[Bahsoun":[77],"&":[78],"G\u00f3ra,":[79],"2005;":[80],"Bahsoun":[81],"et":[82],"al.,":[83],"2005].":[84]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}