{"id":"https://openalex.org/W2023225829","doi":"https://doi.org/10.1109/cdc.2014.7039529","title":"Stabilization of a quasi-linear parabolic Cauchy problem associated with ergodic control of diffusions","display_name":"Stabilization of a quasi-linear parabolic Cauchy problem associated with ergodic control of diffusions","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W2023225829","doi":"https://doi.org/10.1109/cdc.2014.7039529","mag":"2023225829"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2014.7039529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2014.7039529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"53rd IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5022435379","display_name":"Ari Arapostathis","orcid":"https://orcid.org/0000-0003-2207-357X"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ari Arapostathis","raw_affiliation_strings":["Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas","Electrical and Computer Engineering, The University of Texas at Austin, 78703, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Electrical and Computer Engineering, The University of Texas at Austin, 78703, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018541798","display_name":"Vivek S. Borkar","orcid":"https://orcid.org/0000-0003-0756-5402"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vivek S. Borkar","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology, Powai, Mumbai, India","Department of Electrical Engineering Indian Institute of Technology Powai, Mumbai 400076, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology, Powai, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Electrical Engineering Indian Institute of Technology Powai, Mumbai 400076, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109977608","display_name":"K. Suresh Kumar","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. Suresh Kumar","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Powai, Mumbai, India","Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400076, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Powai, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400076, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022435379"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10878051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"1103","last_page":"1110"},"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":0.9959999918937683,"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":0.9959999918937683,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7590082883834839},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.702126145362854},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.6143754720687866},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5838258862495422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5660972595214844},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.5630291104316711},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5396457314491272},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5137563943862915},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.4630487263202667},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43320363759994507},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41751617193222046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3841210901737213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3425326943397522},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.31446877121925354},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23513534665107727},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07665205001831055}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7590082883834839},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.702126145362854},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.6143754720687866},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5838258862495422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5660972595214844},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.5630291104316711},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5396457314491272},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5137563943862915},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.4630487263202667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43320363759994507},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41751617193222046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3841210901737213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3425326943397522},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.31446877121925354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23513534665107727},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07665205001831055},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2014.7039529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2014.7039529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"53rd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1417123979","https://openalex.org/W1513091520","https://openalex.org/W1583562272","https://openalex.org/W1801245917","https://openalex.org/W1998598781","https://openalex.org/W1998862242","https://openalex.org/W1999897837","https://openalex.org/W2011818548","https://openalex.org/W2028836744","https://openalex.org/W2043496299","https://openalex.org/W2059483844","https://openalex.org/W2060116429","https://openalex.org/W2061075226","https://openalex.org/W2072444746","https://openalex.org/W2081374871","https://openalex.org/W2154204727","https://openalex.org/W2567470922","https://openalex.org/W3099885902","https://openalex.org/W3103273170","https://openalex.org/W3104008696","https://openalex.org/W3104160683","https://openalex.org/W6731164432"],"related_works":["https://openalex.org/W2078366360","https://openalex.org/W2400581667","https://openalex.org/W2049761058","https://openalex.org/W4213342640","https://openalex.org/W2394174381","https://openalex.org/W4394654496","https://openalex.org/W2020390959","https://openalex.org/W2345019225","https://openalex.org/W2503576560","https://openalex.org/W1968696210"],"abstract_inverted_index":{"We":[0,44],"study":[1],"the":[2,7,28,56,59,80,83,89],"relative":[3],"value":[4,36],"iteration":[5],"for":[6,17,64],"ergodic":[8,90],"control":[9,91],"problem":[10,37,49],"under":[11],"a":[12,18,31],"near-monotone":[13],"running":[14],"cost":[15],"structure":[16],"nondegenerate":[19],"diffusion":[20],"controlled":[21],"through":[22],"its":[23],"drift.":[24],"This":[25],"algorithm":[26],"takes":[27],"form":[29],"of":[30,58,82],"quasilinear":[32,60],"parabolic":[33,61],"Cauchy":[34,48],"initial":[35,67],"in":[38,52,69],"\u211d":[39],"<sup":[40,71,75],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,72,76],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sup>":[42,77],".":[43],"show":[45],"that":[46,55],"this":[47],"stabilizes,":[50],"or":[51],"other":[53],"words,":[54],"solution":[57,81],"equation":[62,86],"converges":[63],"every":[65],"bounded":[66],"condition":[68],"C":[70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[73],"(\u211d":[74],")":[78],"to":[79],"Hamilton-Jacobi-Bellman":[84],"(HJB)":[85],"associated":[87],"with":[88],"problem.":[92]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}