{"id":"https://openalex.org/W2142044708","doi":"https://doi.org/10.1137/130929965","title":"Stochastic Perron's Method and Elementary Strategies for Zero-Sum Differential Games","display_name":"Stochastic Perron's Method and Elementary Strategies for Zero-Sum Differential Games","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2142044708","doi":"https://doi.org/10.1137/130929965","mag":"2142044708"},"language":"en","primary_location":{"id":"doi:10.1137/130929965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929965","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/A5005194674","display_name":"Mihai \u015c\u0131rbu","orcid":null},"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":"Mihai S\u00eerbu","raw_affiliation_strings":["University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX, 78712"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX, 78712","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005194674"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":11.4609,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.98530384,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"52","issue":"3","first_page":"1693","last_page":"1711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.844657301902771},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.8392900228500366},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.7121170163154602},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5768767595291138},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5330034494400024},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4650633931159973},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.44596022367477417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43952322006225586},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3173147141933441},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3098464012145996}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.844657301902771},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.8392900228500366},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.7121170163154602},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5768767595291138},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5330034494400024},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4650633931159973},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.44596022367477417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43952322006225586},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3173147141933441},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3098464012145996}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130929965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929965","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":[{"id":"https://openalex.org/G2182049188","display_name":"Topics in Stochastic Control and Financial Mathematics","funder_award_id":"1211988","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1497318832","https://openalex.org/W1507126399","https://openalex.org/W1694857287","https://openalex.org/W1963767940","https://openalex.org/W1971594473","https://openalex.org/W1980753586","https://openalex.org/W1985296147","https://openalex.org/W1998407679","https://openalex.org/W2027236047","https://openalex.org/W2032316144","https://openalex.org/W2046047743","https://openalex.org/W2052982373","https://openalex.org/W2055905453","https://openalex.org/W2060627832","https://openalex.org/W2066572496","https://openalex.org/W2088353628","https://openalex.org/W2088471261","https://openalex.org/W2106203939","https://openalex.org/W2117732143","https://openalex.org/W2154825028","https://openalex.org/W2338125180","https://openalex.org/W2888914392","https://openalex.org/W3121250812","https://openalex.org/W3125380953","https://openalex.org/W4243590097"],"related_works":["https://openalex.org/W2766367749","https://openalex.org/W4287078947","https://openalex.org/W2073532336","https://openalex.org/W1654696814","https://openalex.org/W4297940580","https://openalex.org/W4297409026","https://openalex.org/W2088353628","https://openalex.org/W2954291171","https://openalex.org/W2950973671","https://openalex.org/W3124904228"],"abstract_inverted_index":{"We":[0,15],"develop":[1],"here":[2],"the":[3,8,17,20,32,37,51,58,62,77,91,100,105,109,116,122,126,136,140,147,157,161,168,178,183],"stochastic":[4,63,92],"Perron":[5,64,93],"method":[6,65,94],"in":[7,36,61,68],"framework":[9],"of":[10,19,41,99,108,115,125,146,167],"two-player":[11],"zero-sum":[12],"differential":[13],"games.":[14],"consider":[16],"formulation":[18,34],"game":[21,78,184],"where":[22],"both":[23],"players":[24],"play,":[25],"symmetrically,":[26],"feedback":[27,42],"strategies":[28,43],"as":[29,174],"opposed":[30],"to":[31],"Elliott--Kalton":[33],"prevalent":[35],"literature.":[38],"The":[39],"class":[40],"we":[44,75,133],"use":[45],"is":[46,139,172,181],"carefully":[47],"chosen":[48],"so":[49],"that":[50,135],"state":[52],"equation":[53,103,119],"admits":[54],"strong":[55],"solutions":[56],"and":[57,111,142,160],"technicalities":[59],"involved":[60],"carry":[66],"through":[67],"a":[69,96,112,129,175,186],"rather":[70],"simple":[71],"way.":[72],"More":[73],"precisely,":[74],"define":[76],"over":[79,188],"elementary":[80,189],"strategies,":[81],"which":[82],"are":[83],"well":[84],"motivated":[85],"by":[86],"intuition.":[87],"Within":[88],"this":[89],"framework,":[90],"produces":[95],"viscosity":[97,113,130,144],"subsolution":[98],"upper":[101,106,117,123,137,148],"Isaacs":[102,118,149,163,179],"dominating":[104],"value":[107,124,138,159,187],"game,":[110],"supersolution":[114],"lying":[120],"below":[121],"game.":[127],"Using":[128],"comparison":[131],"result":[132],"obtain":[134],"unique":[141],"continuous":[143],"solution":[145],"equation.":[150,164],"An":[151],"identical":[152],"statement":[153],"holds":[154],"true":[155],"for":[156],"lower":[158,162],"A":[165],"version":[166],"dynamic":[169],"programming":[170],"principle":[171],"obtained":[173],"byproduct.":[176],"If":[177],"condition":[180],"satisfied,":[182],"has":[185],"(pure)":[190],"strategies.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
