{"id":"https://openalex.org/W2013341344","doi":"https://doi.org/10.1137/070699408","title":"Convergence of Fourier-Wavelet Models for Gaussian Random Processes","display_name":"Convergence of Fourier-Wavelet Models for Gaussian Random Processes","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2013341344","doi":"https://doi.org/10.1137/070699408","mag":"2013341344"},"language":"en","primary_location":{"id":"doi:10.1137/070699408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699408","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5112317508","display_name":"O. Kurbanmuradov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"O. Kurbanmuradov","raw_affiliation_strings":["kurbanmuradov@wias-berlin.de#TAB#"],"affiliations":[{"raw_affiliation_string":"kurbanmuradov@wias-berlin.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088085508","display_name":"Karl K. Sabelfeld","orcid":"https://orcid.org/0000-0003-3698-7540"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Sabelfeld","raw_affiliation_strings":["sabelfel@wias-berlin.de#TAB#"],"affiliations":[{"raw_affiliation_string":"sabelfel@wias-berlin.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112317508"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7492,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.95807213,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"6","first_page":"3084","last_page":"3112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13244","display_name":"Analysis of environmental and stochastic processes","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13244","display_name":"Analysis of environmental and stochastic processes","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"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/T13193","display_name":"Geological Studies and Exploration","score":0.9276999831199646,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9103999733924866,"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/mathematics","display_name":"Mathematics","score":0.8484017848968506},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.5741907358169556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5091502070426941},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4983792304992676},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49610432982444763},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4949008822441101},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.49428415298461914},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49192214012145996},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.4866069555282593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4620022475719452},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.43513041734695435},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.24076151847839355},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.23254957795143127},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15047070384025574},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08078232407569885},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07003206014633179}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8484017848968506},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.5741907358169556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5091502070426941},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4983792304992676},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49610432982444763},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4949008822441101},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.49428415298461914},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49192214012145996},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.4866069555282593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4620022475719452},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.43513041734695435},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.24076151847839355},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.23254957795143127},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15047070384025574},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08078232407569885},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07003206014633179},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.0},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.0},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070699408","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070699408","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:doi:10.20347/wias.preprint.1239","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00002852","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1523050803","https://openalex.org/W1561428091","https://openalex.org/W1564017276","https://openalex.org/W1575723423","https://openalex.org/W1579647295","https://openalex.org/W1592093959","https://openalex.org/W1965263802","https://openalex.org/W1965597870","https://openalex.org/W1982127533","https://openalex.org/W1984604835","https://openalex.org/W1987721279","https://openalex.org/W1996648727","https://openalex.org/W2003948123","https://openalex.org/W2006776024","https://openalex.org/W2010004355","https://openalex.org/W2010471856","https://openalex.org/W2012956057","https://openalex.org/W2015306612","https://openalex.org/W2023289522","https://openalex.org/W2031947580","https://openalex.org/W2038030613","https://openalex.org/W2044495302","https://openalex.org/W2050831540","https://openalex.org/W2051248491","https://openalex.org/W2060238229","https://openalex.org/W2062024414","https://openalex.org/W2068081918","https://openalex.org/W2079559649","https://openalex.org/W2154003217","https://openalex.org/W2477744154","https://openalex.org/W2484489512","https://openalex.org/W3037934031","https://openalex.org/W3148924112","https://openalex.org/W4300679624"],"related_works":["https://openalex.org/W2482464444","https://openalex.org/W1530855127","https://openalex.org/W2022177602","https://openalex.org/W2779146629","https://openalex.org/W2039045183","https://openalex.org/W2276998430","https://openalex.org/W4253827225","https://openalex.org/W4234980991","https://openalex.org/W3095868147","https://openalex.org/W4242489673"],"abstract_inverted_index":{"Mean":[0],"square":[1,60],"convergence":[2,4,36,54],"and":[3,26],"in":[5,16,27,38,57,62],"probability":[6],"of":[7,11,19,22,41,53,55],"Fourier-wavelet":[8],"models":[9],"(FWM)":[10],"stationary":[12],"Gaussian":[13],"random":[14],"processes":[15],"the":[17,35,39,50,58,63],"metric":[18],"Banach":[20],"space":[21,29],"continuously":[23],"differentiable":[24],"functions":[25,43],"Sobolev":[28],"are":[30,44],"studied.":[31],"Sufficient":[32],"conditions":[33],"for":[34],"formulated":[37],"frame":[40],"spectral":[42],"given.":[45],"It":[46],"is":[47],"shown":[48],"that":[49],"given":[51],"rates":[52],"FWM":[56],"mean":[59],"obtained":[61],"Nikolski\u2013Besov":[64],"classes":[65],"cannot":[66],"be":[67],"improved.":[68]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
