{"id":"https://openalex.org/W1980130100","doi":"https://doi.org/10.1137/s0363012998344270","title":"Approximation of the Kushner Equation for Nonlinear Filtering","display_name":"Approximation of the Kushner Equation for Nonlinear Filtering","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1980130100","doi":"https://doi.org/10.1137/s0363012998344270","mag":"1980130100"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012998344270","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998344270","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/A5004826461","display_name":"Kazufumi Ito","orcid":"https://orcid.org/0000-0003-2417-2600"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kazufumi Ito","raw_affiliation_strings":["North Carolina State University,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University,","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044537548","display_name":"B. L. Rozovski\u012d","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I2800817003","display_name":"California Southern University","ror":"https://ror.org/058zz0t50","country_code":"US","type":"education","lineage":["https://openalex.org/I2800817003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris Rozovskii","raw_affiliation_strings":["University of Southern California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I2800817003","https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9867,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.93812434,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"3","first_page":"893","last_page":"915"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9930999875068665,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9890000224113464,"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":0.8500977754592896},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.7475236058235168},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6606521010398865},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5847971439361572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5030247569084167},{"id":"https://openalex.org/keywords/filtering-problem","display_name":"Filtering problem","score":0.5018370151519775},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.47684991359710693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4274412989616394},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.12453541159629822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09454497694969177}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8500977754592896},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.7475236058235168},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6606521010398865},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5847971439361572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5030247569084167},{"id":"https://openalex.org/C41614226","wikidata":"https://www.wikidata.org/wiki/Q5449244","display_name":"Filtering problem","level":4,"score":0.5018370151519775},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.47684991359710693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4274412989616394},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.12453541159629822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09454497694969177},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012998344270","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998344270","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W23051277","https://openalex.org/W133664551","https://openalex.org/W144595045","https://openalex.org/W1964377184","https://openalex.org/W1966601420","https://openalex.org/W2024900789","https://openalex.org/W2033736734","https://openalex.org/W2058901392","https://openalex.org/W2065450136","https://openalex.org/W2085495436","https://openalex.org/W2094011292","https://openalex.org/W2094060968","https://openalex.org/W2178464435","https://openalex.org/W2498465090","https://openalex.org/W2506877196","https://openalex.org/W2798556646","https://openalex.org/W3021064114","https://openalex.org/W4301283118","https://openalex.org/W4302367620"],"related_works":["https://openalex.org/W4234874385","https://openalex.org/W2323648130","https://openalex.org/W2157140558","https://openalex.org/W2378782423","https://openalex.org/W4233308809","https://openalex.org/W2318982644","https://openalex.org/W2388988621","https://openalex.org/W412354254","https://openalex.org/W1873850890","https://openalex.org/W4379522615"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,33],"discuss":[4,34],"the":[5,12,29,38,42],"well-posedness":[6],"and":[7,21],"approximation":[8],"of":[9],"solutions":[10],"to":[11,37],"Kushner":[13],"equation":[14],"in":[15],"nonlinear":[16],"filtering":[17],"problems.":[18],"We":[19],"develop":[20],"analyze":[22],"a":[23],"time":[24],"integration":[25],"method":[26,40],"based":[27],"on":[28],"operator":[30],"splitting.":[31],"Also,":[32],"its":[35],"relation":[36],"operator-splitting":[39],"for":[41],"Zakai":[43],"equation.":[44]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
