{"id":"https://openalex.org/W2091896264","doi":"https://doi.org/10.1137/100816936","title":"Stochastic Comparison, Boundedness, Weak Convergence, and Ergodicity of a Random Riccati Equation with Markovian Binary Switching","display_name":"Stochastic Comparison, Boundedness, Weak Convergence, and Ergodicity of a Random Riccati Equation with Markovian Binary Switching","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2091896264","doi":"https://doi.org/10.1137/100816936","mag":"2091896264"},"language":"en","primary_location":{"id":"doi:10.1137/100816936","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100816936","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5019177114","display_name":"Li Xie","orcid":"https://orcid.org/0000-0002-5214-9769"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li Xie","raw_affiliation_strings":["xieli.lixie@gmail.com#TAB#"],"affiliations":[{"raw_affiliation_string":"xieli.lixie@gmail.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019177114"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4224581,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.94512941,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"1","first_page":"532","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9076150059700012},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6107867956161499},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.5884443521499634},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.559968113899231},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.5203549265861511},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5082458853721619},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.49163299798965454},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.42262938618659973},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31415289640426636},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2909415364265442},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0953124463558197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9076150059700012},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6107867956161499},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.5884443521499634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.559968113899231},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5203549265861511},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5082458853721619},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.49163299798965454},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.42262938618659973},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31415289640426636},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2909415364265442},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0953124463558197},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100816936","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100816936","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1981984734","https://openalex.org/W1988868967","https://openalex.org/W1992356180","https://openalex.org/W2034525806","https://openalex.org/W2065363913","https://openalex.org/W2092630498","https://openalex.org/W2118048279","https://openalex.org/W2140355755","https://openalex.org/W2152898444","https://openalex.org/W2164522996","https://openalex.org/W2165777968","https://openalex.org/W4249303767"],"related_works":["https://openalex.org/W1972942382","https://openalex.org/W2009962825","https://openalex.org/W1722744795","https://openalex.org/W124275629","https://openalex.org/W2136727990","https://openalex.org/W2950014027","https://openalex.org/W2952991236","https://openalex.org/W964575223","https://openalex.org/W4296948412","https://openalex.org/W2358718285"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,29,57,66,82,86,90,96,116,119,127,137,150],"dynamical":[4],"behavior":[5],"of":[6,26,28,68,98,118,121,136,149],"a":[7,18,73,110,147,154],"discrete-time":[8],"random":[9,30,52],"Riccati":[10,31,53],"equation":[11,32],"with":[12,21],"Markovian":[13],"binary":[14],"switching":[15],"arising":[16],"from":[17],"Kalman":[19],"filter":[20],"intermittent":[22],"observations.":[23],"A":[24,44],"number":[25],"properties":[27,105],"are":[33,93],"studied":[34],"such":[35],"as":[36],"comparability,":[37],"monotonicity,":[38],"boundedness,":[39],"weak":[40,99],"convergence,":[41],"and":[42,55,84,89,101,115,129,139],"ergodicity.":[43],"stochastic":[45],"order":[46],"method":[47],"is":[48],"used":[49],"to":[50,95,108],"compare":[51],"equations":[54],"establish":[56,109],"monotonicity":[58],"property":[59],"in":[60,142,157],"an":[61,77],"expectation":[62,78,120],"sense.":[63],"By":[64,133],"using":[65],"idea":[67],"stopping":[69],"times,":[70],"we":[71,145],"present":[72,146],"sufficient":[74],"condition":[75],"for":[76],"boundedness":[79,140],"property.":[80],"Moreover,":[81],"contraction":[83],"nonexpansion,":[85],"Riemannian":[87],"metric,":[88],"Markov\u2013Feller":[91],"operator":[92],"applied":[94],"analysis":[97],"convergence":[100],"ergodicity":[102],"properties.":[103],"These":[104],"allow":[106],"us":[107],"relation":[111],"between":[112],"time":[113],"average":[114],"limit":[117],"covariance":[122],"matrices.":[123],"We":[124],"also":[125],"revisit":[126],"independently":[128],"identically":[130],"distributed":[131],"case.":[132],"making":[134],"use":[135],"comparison":[138],"results":[141],"this":[143],"paper,":[144],"variant":[148],"existence":[151],"theorem":[152],"about":[153],"critical":[155],"value":[156],"existing":[158],"literature.":[159]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}