{"id":"https://openalex.org/W2010737928","doi":"https://doi.org/10.1137/s1064827503424505","title":"Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure","display_name":"Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2010737928","doi":"https://doi.org/10.1137/s1064827503424505","mag":"2010737928"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503424505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503424505","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00686211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003805312","display_name":"Christian Soize","orcid":"https://orcid.org/0000-0002-1083-6771"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Soize","raw_affiliation_strings":["Laboratoire de M\u00e9canique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de M\u00e9canique","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006138292","display_name":"Roger Ghanem","orcid":"https://orcid.org/0000-0002-1890-920X"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roger Ghanem","raw_affiliation_strings":["Johns Hopkins University ("],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University (","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.8635,"has_fulltext":false,"cited_by_count":588,"citation_normalized_percentile":{"value":0.98575454,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"26","issue":"2","first_page":"395","last_page":"410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11874","display_name":"Structural Response to Dynamic Loads","score":0.9463000297546387,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7969931364059448},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6770327091217041},{"id":"https://openalex.org/keywords/random-element","display_name":"Random element","score":0.6323872208595276},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.6069726347923279},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.6061683893203735},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.5657821297645569},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5535677671432495},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5527405738830566},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5345417857170105},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.4867851436138153},{"id":"https://openalex.org/keywords/algebra-of-random-variables","display_name":"Algebra of random variables","score":0.4684104323387146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42402881383895874},{"id":"https://openalex.org/keywords/product-measure","display_name":"Product measure","score":0.42113468050956726},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4111328125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29922378063201904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25695890188217163},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20887336134910583},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10146668553352356},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.08761894702911377},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07299324870109558}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7969931364059448},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6770327091217041},{"id":"https://openalex.org/C52386014","wikidata":"https://www.wikidata.org/wiki/Q166211","display_name":"Random element","level":3,"score":0.6323872208595276},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6069726347923279},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.6061683893203735},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.5657821297645569},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5535677671432495},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5527405738830566},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5345417857170105},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.4867851436138153},{"id":"https://openalex.org/C89231458","wikidata":"https://www.wikidata.org/wiki/Q4723976","display_name":"Algebra of random variables","level":4,"score":0.4684104323387146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42402881383895874},{"id":"https://openalex.org/C55606962","wikidata":"https://www.wikidata.org/wiki/Q1572094","display_name":"Product measure","level":3,"score":0.42113468050956726},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4111328125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29922378063201904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25695890188217163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20887336134910583},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10146668553352356},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.08761894702911377},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07299324870109558},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827503424505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503424505","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.472.2785","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.2785","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/68/62/11/PDF/publi-2004-SIAM-28_2_395-410-soize-ghanem-preprint.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00686211v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00686211","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2004, 26 (2), pp.395-410. ⟨10.1137/S1064827503424505⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00686211v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00686211","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2004, 26 (2), pp.395-410. ⟨10.1137/S1064827503424505⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W109843813","https://openalex.org/W591296147","https://openalex.org/W1483560004","https://openalex.org/W1538934584","https://openalex.org/W1571308994","https://openalex.org/W1571984195","https://openalex.org/W1588513474","https://openalex.org/W1971746901","https://openalex.org/W1979367451","https://openalex.org/W1988859494","https://openalex.org/W2003191951","https://openalex.org/W2004515370","https://openalex.org/W2044686842","https://openalex.org/W2056099894","https://openalex.org/W2056145867","https://openalex.org/W2086077633","https://openalex.org/W2089770162","https://openalex.org/W2160786691","https://openalex.org/W2167720109","https://openalex.org/W2321957512","https://openalex.org/W2484588736","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W121312646","https://openalex.org/W1995336439","https://openalex.org/W3195391652","https://openalex.org/W4246232962","https://openalex.org/W2183541783","https://openalex.org/W2005105399","https://openalex.org/W2389966714","https://openalex.org/W2383059660","https://openalex.org/W2154781922","https://openalex.org/W2010737928"],"abstract_inverted_index":{"Abstract.":[0],"The":[1],"basic":[2,50,82],"random":[3,7,51,74,83],"variables":[4,84],"on":[5,41,88],"which":[6,26],"uncertainties":[8],"can":[9,15,33,95],"in":[10,112],"a":[11,20,42],"given":[12],"model":[13],"depend":[14],"be":[16,34,96],"viewed":[17,97],"as":[18,98],"defining":[19],"measure":[21,37,44],"space":[22,38,61,91,114],"with":[23,46,70,118],"respect":[24],"to":[25,29,65],"the":[27,30,47,56,66,73,89,101,119],"solution":[28],"mathe-matical":[31],"problem":[32],"defined.":[35],"This":[36,53],"is":[39],"defined":[40],"product":[43,90],"associated":[45,69,120],"collection":[48],"of":[49,59,72,77,100,110],"variables.":[52,75],"paper":[54],"clarifies":[55],"mathematical":[57],"structure":[58],"this":[60,113],"and":[62,80],"its":[63],"relationship":[64],"underlying":[67],"spaces":[68],"each":[71],"Cases":[76],"both":[78],"dependent":[79],"independent":[81],"are":[85,92,115],"addressed.":[86],"Bases":[87],"developed":[93],"that":[94],"generalizations":[99],"standard":[102],"polynomial":[103],"chaos":[104],"approximation.":[105],"Moreover,":[106],"two":[107],"numerical":[108],"constructions":[109],"approximations":[111],"presented":[116],"along":[117],"convergence":[121],"analysis.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":27},{"year":2024,"cited_by_count":31},{"year":2023,"cited_by_count":28},{"year":2022,"cited_by_count":35},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":35},{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":45},{"year":2017,"cited_by_count":52},{"year":2016,"cited_by_count":31},{"year":2015,"cited_by_count":36},{"year":2014,"cited_by_count":29},{"year":2013,"cited_by_count":29},{"year":2012,"cited_by_count":28}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}