{"id":"https://openalex.org/W1490150974","doi":"https://doi.org/10.1007/978-1-4612-4482-0","title":"Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems","display_name":"Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W1490150974","doi":"https://doi.org/10.1007/978-1-4612-4482-0","mag":"1490150974"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4612-4482-0","doi":"https://doi.org/10.1007/978-1-4612-4482-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-4482-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"book"},"volume":null,"type":"book","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/A5112058612","display_name":"Harold J. Kushner","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Harold J. Kushner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112058612"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.2966,"has_fulltext":false,"cited_by_count":286,"citation_normalized_percentile":{"value":0.97382199,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.7759000062942505,"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":0.7759000062942505,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.1096000000834465,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.013299999758601189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.8840000033378601},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"singular perturbation","score":0.7760000228881836},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"stochastic control","score":0.8840000033378601},{"id":"https://openalex.org/keywords/nonlinear-filtering","display_name":"nonlinear filtering","score":0.7910000085830688},{"id":"https://openalex.org/keywords/jump-diffusion-processes","display_name":"jump-diffusion processes","score":0.7200000286102295},{"id":"https://openalex.org/keywords/martingale-problem","display_name":"martingale problem","score":0.875},{"id":"https://openalex.org/keywords/relaxed-controls","display_name":"relaxed controls","score":0.7369999885559082},{"id":"https://openalex.org/keywords/occupation-measures","display_name":"occupation measures","score":0.7059999704360962},{"id":"https://openalex.org/keywords/reflected-diffusion","display_name":"reflected diffusion","score":0.7860000133514404},{"id":"https://openalex.org/keywords/optimal-stopping","display_name":"optimal stopping","score":0.6800000071525574},{"id":"https://openalex.org/keywords/average-cost-per-unit-time","display_name":"average cost per unit time","score":0.9240000247955322},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.593999981880188},{"id":"https://openalex.org/keywords/measure-valued-processes","display_name":"measure-valued processes","score":0.7149999737739563},{"id":"https://openalex.org/keywords/ito-s-formula","display_name":"It\u00f4 formula","score":0.6859999895095825},{"id":"https://openalex.org/keywords/martingales","display_name":"martingales","score":0.7559999823570251},{"id":"https://openalex.org/keywords/stochastic-integrals","display_name":"stochastic integration","score":0.5590000152587891}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6960545778274536},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.45702502131462097},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4326501786708832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4275383949279785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4257558584213257},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3922909200191498},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32558587193489075},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.16464510560035706},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10525479912757874},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-1-4612-4482-0","doi":"https://doi.org/10.1007/978-1-4612-4482-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-4482-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"book"},{"id":"pmh:oai:cds.cern.ch:1611849","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/1611849","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2740707752","https://openalex.org/W2092222583","https://openalex.org/W2955011714","https://openalex.org/W4254036705","https://openalex.org/W2062430834","https://openalex.org/W2078382051","https://openalex.org/W2000541672","https://openalex.org/W2062736751","https://openalex.org/W2955604483","https://openalex.org/W1975594474"],"abstract_inverted_index":{"1":[0],"Weak":[1,122,301,331,357,441],"Convergence.-":[2,332,442],"0.":[3,44,97,131,181,226,308,345,384,431],"Outline":[4,45,98,132,182,227,309,346,385,432],"of":[5,46,68,99,133,144,183,193,210,228,234,251,266,278,310,335,347,359,386,395,433,447],"the":[6,47,100,134,145,184,211,229,235,243,252,259,267,279,288,296,311,336,348,360,366,387,434],"Chapter.-":[7,48,101,135,185,230,312,349,388,435],"1.":[8,49,102,136,186,231,313,350,389,436],"Basic":[9],"Properties":[10],"and":[11,38,54,124,148,154,174,273,330,353],"Definitions.-":[12],"2.":[13,51,106,142,191,238,316,356,398,443],"Examples.-":[14],"3.":[15,57,111,151,199,247,323,363,406],"The":[16,20,27,79,88,116,200,222,239,248,263,292,303,317,324,351,370,374,413],"Skorohod":[17],"Representation.-":[18],"4.":[19,62,115,158,203,255,333,369,412],"Function":[21,28,306,320,327],"Space":[22,29],"Ck":[23],"[0,":[24,31],"T].-":[25,32],"5.":[26,70,120,164,208,262,373,416],"Dk":[30],"6.":[33,78,167,214,270,420],"Measure":[34,187],"Valued":[35,188],"Random":[36,189],"Variables":[37],"Processes.-":[39,84,166],"2":[40],"Stochastic":[41,52,58,64,76,94,112],"Processes:":[42,87,410,440],"Background.-":[43],"Martingales.-":[50],"Integrals":[53],"Ito's":[55],"Lemma.-":[56],"Differential":[59,65,95],"Equations:":[60,66],"Bounds.-":[61],"Controlled":[63,93,103,127],"Existence":[67],"Solutions.-":[69],"Representing":[71],"a":[72,75],"Martingale":[73,80,89,117],"as":[74],"Integral.-":[77],"Problem.-":[81,202,220,225,380],"7.":[82,217,276],"Jump-Diffusion":[83,86,165,393],"8.":[85,282],"Problem":[90,118,137,241],"Formulation.-":[91],"3":[92],"Equations.-":[96],"S.D.E.'s:":[104],"Introduction.-":[105,322],"Relaxed":[107,113],"Controls:":[108],"Deterministic":[109,401],"Case.-":[110,415],"Controls.-":[114],"Revisited.-":[119],"Approximations,":[121],"Convergence":[123,358,364],"Optimality.-":[125],"4":[126],"Singularly":[128,204,244,339,399,407,421,437],"Perturbed":[129,205,245,304,318,325,340,400,408,422,438],"Systems.-":[130,344,427],"Formulation:":[138],"Finite":[139],"Time":[140,179,298,379],"Interval.-":[141,299],"Approximation":[143,286],"Optimal":[146,155],"Controls":[147],"Value":[149],"Functions.-":[150],"Discounted":[152,218],"Cost":[153,160,176,219,376],"Stopping":[156],"Problems.-":[157,180,207],"Average":[159,175,375],"Per":[161,177,377],"Unit":[162,178,378],"Time.-":[163],"Other":[168],"Approaches.-":[169],"5":[170],"Functional":[171,194],"Occupation":[172,195],"Measures":[173,196],"Variables.-":[190],"Limits":[192],"for":[197,242,392],"Diffusions.-":[198,216],"Control":[201,206,209],"Fast":[212,361],"System.-":[213,246,362,368],"Reflected":[215],"6":[221],"Nonlinear":[223,236],"Filtering":[224,240],"A":[232,256,271,283],"Representation":[233],"Filter.-":[237,254,261,269,290],"Almost":[249],"Optimality":[250,265,371],"Averaged":[253,260,268,280,289,293,367],"Counterexample":[257],"to":[258,287,365],"Near":[264],"Repair":[272],"Maintainance":[274],"Example.-":[275,315],"Robustness":[277],"Filters.-":[281],"Robust":[284],"Computational":[285],"9.":[291],"Filter":[294],"on":[295,404],"Infinite":[297],"7":[300],"Convergence:":[302],"Test":[305,319,326],"Method.-":[307],"An":[314],"Method:":[321,328],"Tightness":[329],"Characterization":[334],"Limits.-":[337],"8":[338],"Wide-Band":[341],"Noise":[342,354,425],"Driven":[343,426],"System":[352],"Model.-":[355],"Theorem.-":[372],"9":[381],"Stability":[382,390],"Theory.-":[383],"Theory":[391],"Processes":[394],"Ito":[396,409,439],"Type.-":[397],"Systems:":[402],"Bounds":[403],"Paths.-":[405],"Tightness.-":[411],"Linear":[414],"Wide":[417,423],"Bandwidth":[418,424],"Noise.-":[419],"10":[428],"Parametric":[429],"Singularities.-":[430],"Stability.-":[444],"References.-":[445],"List":[446],"Symbols.":[448]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":19}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
