{"id":"https://openalex.org/W2300515143","doi":"https://doi.org/10.1007/s00041-017-9539-5","title":"Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients","display_name":"Representations of Gaussian Random Fields and Approximation of Elliptic PDEs with Lognormal Coefficients","publication_year":2017,"publication_date":"2017-03-29","ids":{"openalex":"https://openalex.org/W2300515143","doi":"https://doi.org/10.1007/s00041-017-9539-5","mag":"2300515143"},"language":"en","primary_location":{"id":"doi:10.1007/s00041-017-9539-5","doi":"https://doi.org/10.1007/s00041-017-9539-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00041-017-9539-5","pdf_url":null,"source":{"id":"https://openalex.org/S179905963","display_name":"Journal of Fourier Analysis and Applications","issn_l":"1069-5869","issn":["1069-5869","1531-5851"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-2","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Fourier Analysis and Applications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1603.05559","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017726844","display_name":"Markus Bachmayr","orcid":"https://orcid.org/0000-0002-8051-2270","observed_orcids":["https://orcid.org/0000-0002-8051-2270"]},"institutions":[{"id":"https://openalex.org/I4210086928","display_name":"Institute of Numerical Mathematics","ror":"https://ror.org/00520ey40","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210086928","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":"DE","type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}],"countries":["DE","RU"],"is_corresponding":true,"raw_author_name":"Markus Bachmayr","raw_affiliation_strings":["Hausdorff Center for Mathematics, Institute for Numerical Simulation, Endenicher Allee 60, 53115, Bonn, Germany","Institute for Numerical Simulation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics, Institute for Numerical Simulation, Endenicher Allee 60, 53115, Bonn, Germany","institution_ids":["https://openalex.org/I4391767997"]},{"raw_affiliation_string":"Institute for Numerical Simulation","institution_ids":["https://openalex.org/I4210086928"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108445641","display_name":"Albert K. Cohen","orcid":"https://orcid.org/0000-0003-1337-4012","observed_orcids":["https://orcid.org/0000-0003-1337-4012","https://orcid.org/0000-0002-8866-5343"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Albert Cohen","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598, 4 place Jussieu, 75005, Paris, France","Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598, 4 place Jussieu, 75005, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I4405264447"]},{"raw_affiliation_string":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4405264447"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059030374","display_name":"Giovanni Migliorati","orcid":"https://orcid.org/0000-0002-6317-5663","observed_orcids":["https://orcid.org/0000-0002-6317-5663"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Giovanni Migliorati","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598, 4 place Jussieu, 75005, Paris, France","Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598, 4 place Jussieu, 75005, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I4405264447"]},{"raw_affiliation_string":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, CNRS, UMR 7598","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4405264447"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5017726844"],"corresponding_institution_ids":["https://openalex.org/I4210086928","https://openalex.org/I4391767997"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":3.183,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.91230811,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"3","first_page":"621","last_page":"649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.23180000483989716,"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":0.23180000483989716,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.10559999942779541,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.0957999974489212,"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/gaussian-random-fields","display_name":"Gaussian random fields","score":0.8019999861717224},{"id":"https://openalex.org/keywords/stationary-random-fields","display_name":"stationary random fields","score":0.7570000290870667},{"id":"https://openalex.org/keywords/karhunen-loeve-expansion","display_name":"Karhunen-Loeve transform","score":0.8259999752044678},{"id":"https://openalex.org/keywords/polynomial-approximation","display_name":"polynomial approximation","score":0.7039999961853027},{"id":"https://openalex.org/keywords/matern-covariance-function","display_name":"Mat\u00e9rn covariance","score":0.8629999756813049},{"id":"https://openalex.org/keywords/periodic-extension","display_name":"periodic extension","score":0.8579999804496765},{"id":"https://openalex.org/keywords/circulant-embedding","display_name":"circulant embedding","score":0.8019999861717224},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.5540000200271606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7647614479064941},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.6944969296455383},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6019498109817505},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.572318971157074},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5358375906944275},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.506025493144989},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45103251934051514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3898579478263855},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3447258472442627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32953816652297974},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11969774961471558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08144786953926086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00041-017-9539-5","doi":"https://doi.org/10.1007/s00041-017-9539-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00041-017-9539-5","pdf_url":null,"source":{"id":"https://openalex.org/S179905963","display_name":"Journal of Fourier Analysis and Applications","issn_l":"1069-5869","issn":["1069-5869","1531-5851"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-2","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Fourier Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1603.05559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1603.05559","pdf_url":"https://arxiv.org/pdf/1603.05559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2300515143","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1603.05559.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01352284v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-01352284","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"Journal of Fourier Analysis and Applications, 2018, 24, pp.621-649","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1603.05559","doi":"https://doi.org/10.48550/arxiv.1603.05559","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.05559","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1603.05559","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1603.05559","pdf_url":"https://arxiv.org/pdf/1603.05559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2300515143.pdf","grobid_xml":"https://content.openalex.org/works/W2300515143.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W624584418","https://openalex.org/W835076124","https://openalex.org/W1966606705","https://openalex.org/W1984604835","https://openalex.org/W1986280275","https://openalex.org/W2008058003","https://openalex.org/W2026237857","https://openalex.org/W2051344283","https://openalex.org/W2052271668","https://openalex.org/W2067111814","https://openalex.org/W2072282162","https://openalex.org/W2079559649","https://openalex.org/W2080348404","https://openalex.org/W2115125420","https://openalex.org/W2125942255","https://openalex.org/W2170826679","https://openalex.org/W2464287708","https://openalex.org/W2474000053","https://openalex.org/W2995924920","https://openalex.org/W4231428347","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W3137703578","https://openalex.org/W4404976328","https://openalex.org/W2062993069","https://openalex.org/W2965734800","https://openalex.org/W4414633426","https://openalex.org/W2049222546","https://openalex.org/W7099189274","https://openalex.org/W6927230878","https://openalex.org/W2170826679","https://openalex.org/W2739586169"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2016-06-24T00:00:00"}
