{"id":"https://openalex.org/W7127913972","doi":"https://doi.org/10.31861/bmj2026.02.05","title":"Estimation of reliability and accuracy of models of $\\varphi$-sub-Gaussian process in $L_p(T)$ using generating functions of polynomial expansions","display_name":"Estimation of reliability and accuracy of models of $\\varphi$-sub-Gaussian process in $L_p(T)$ using generating functions of polynomial expansions","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7127913972","doi":"https://doi.org/10.31861/bmj2026.02.05"},"language":"en","primary_location":{"id":"doi:10.31861/bmj2026.02.05","doi":"https://doi.org/10.31861/bmj2026.02.05","is_oa":true,"landing_page_url":"https://doi.org/10.31861/bmj2026.02.05","pdf_url":"https://media.chnu.edu.ua/media/duudvng1/55-69-mokliachuk_novyi.pdf","source":{"id":"https://openalex.org/S4210220162","display_name":"Bukovinian Mathematical Journal","issn_l":"2309-4001","issn":["2309-4001","3083-7545"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321237","host_organization_name":"Yuriy Fedkovych Chernivtsi National University","host_organization_lineage":["https://openalex.org/P4310321237"],"host_organization_lineage_names":["Yuriy Fedkovych Chernivtsi National University"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bukovinian Mathematical Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://media.chnu.edu.ua/media/duudvng1/55-69-mokliachuk_novyi.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052428015","display_name":"Oleksandr Mokliachuk","orcid":"https://orcid.org/0000-0002-4962-774X","observed_orcids":["https://orcid.org/0000-0002-4962-774X"]},"institutions":[{"id":"https://openalex.org/I4210122812","display_name":"Sun Pharma (United States)","ror":"https://ror.org/02f5ccn55","country_code":"US","type":"company","lineage":["https://openalex.org/I4210122812"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Oleksandr Mokliachuk","raw_affiliation_strings":["Sun Pharma (United States)"],"raw_orcid":"https://orcid.org/0000-0002-4962-774X","affiliations":[{"raw_affiliation_string":"Sun Pharma (United States)","institution_ids":["https://openalex.org/I4210122812"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052428015"],"corresponding_institution_ids":["https://openalex.org/I4210122812"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09825754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"55","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9307000041007996,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9307000041007996,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.015399999916553497,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.011300000362098217,"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/generating-functions","display_name":"generating functions","score":0.7689999938011169},{"id":"https://openalex.org/keywords/truncation-error","display_name":"truncation error","score":0.8309999704360962},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.968999981880188},{"id":"https://openalex.org/keywords/generalized-laguerre-polynomials","display_name":"generalized Laguerre polynomials","score":0.9890000224113464},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":1.0}],"concepts":[{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.7005000114440918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6051999926567078},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5827999711036682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5745999813079834},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5408999919891357},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3849000036716461},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.36239999532699585},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3122999966144562},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C109308471","wikidata":"https://www.wikidata.org/wiki/Q2046647","display_name":"Karhunen\u2013Lo\u00e8ve theorem","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29120001196861267},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.25519999861717224},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.31861/bmj2026.02.05","doi":"https://doi.org/10.31861/bmj2026.02.05","is_oa":true,"landing_page_url":"https://doi.org/10.31861/bmj2026.02.05","pdf_url":"https://media.chnu.edu.ua/media/duudvng1/55-69-mokliachuk_novyi.pdf","source":{"id":"https://openalex.org/S4210220162","display_name":"Bukovinian Mathematical Journal","issn_l":"2309-4001","issn":["2309-4001","3083-7545"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321237","host_organization_name":"Yuriy Fedkovych Chernivtsi National University","host_organization_lineage":["https://openalex.org/P4310321237"],"host_organization_lineage_names":["Yuriy Fedkovych Chernivtsi National University"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bukovinian Mathematical Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2602.04668","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.04668","pdf_url":"https://arxiv.org/pdf/2602.04668","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":"doi:10.48550/arxiv.2602.04668","doi":"https://doi.org/10.48550/arxiv.2602.04668","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.04668","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":"doi:10.31861/bmj2026.02.05","doi":"https://doi.org/10.31861/bmj2026.02.05","is_oa":true,"landing_page_url":"https://doi.org/10.31861/bmj2026.02.05","pdf_url":"https://media.chnu.edu.ua/media/duudvng1/55-69-mokliachuk_novyi.pdf","source":{"id":"https://openalex.org/S4210220162","display_name":"Bukovinian Mathematical Journal","issn_l":"2309-4001","issn":["2309-4001","3083-7545"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321237","host_organization_name":"Yuriy Fedkovych Chernivtsi National University","host_organization_lineage":["https://openalex.org/P4310321237"],"host_organization_lineage_names":["Yuriy Fedkovych Chernivtsi National University"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bukovinian Mathematical Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328070","display_name":"Sun Pharma","ror":"https://ror.org/04vnqkx80"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127913972.pdf","grobid_xml":"https://content.openalex.org/works/W7127913972.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W242065599","https://openalex.org/W1482235099","https://openalex.org/W1538934584","https://openalex.org/W2030997677","https://openalex.org/W2051939984","https://openalex.org/W2108629272","https://openalex.org/W2754837711","https://openalex.org/W4319340075"],"related_works":["https://openalex.org/W6891919742","https://openalex.org/W2754837711","https://openalex.org/W7112800634","https://openalex.org/W2094149917","https://openalex.org/W4220777248","https://openalex.org/W4403498650","https://openalex.org/W4415031215","https://openalex.org/W1764409322","https://openalex.org/W4234979286","https://openalex.org/W2015937695"],"abstract_inverted_index":{"Stochastic":[0],"processes":[1],"are":[2,57,115],"often":[3],"represented":[4],"through":[5],"orthonormal":[6,92],"series":[7,141],"expansions,":[8],"a":[9,153],"framework":[10],"originating":[11],"in":[12,31,69,102,119],"the":[13,49,70,74,89,106,138],"classical":[14],"works":[15],"of":[16,45,51,62,140,148,156],"Lo\\`eve":[17],"and":[18,20,25,80,110,127,150],"Karhunen":[19],"widely":[21],"used":[22],"for":[23,83,117,125,136],"simulation":[24],"numerical":[26],"approximation.":[27,129],"While":[28],"truncation":[29,126],"error":[30,46],"such":[32],"expansions":[33],"has":[34],"been":[35],"extensively":[36],"studied,":[37],"practical":[38,134],"models":[39,118],"frequently":[40],"involve":[41],"an":[42],"additional":[43],"source":[44],"arising":[47],"from":[48],"approximation":[50],"coefficient":[52,128],"functions":[53,101],"when":[54],"closed-form":[55],"expressions":[56],"unavailable.":[58],"The":[59,130],"combined":[60],"effect":[61],"these":[63],"two":[64],"errors":[65],"remains":[66],"insufficiently":[67],"addressed":[68],"literature.":[71],"Building":[72],"on":[73,78],"author's":[75],"earlier":[76],"work":[77],"reliability":[79,149],"accuracy":[81,151],"estimates":[82],"$\\varphi$-sub-Gaussian":[84],"processes,":[85],"this":[86],"paper":[87],"extends":[88],"methodology":[90],"to":[91,144],"polynomial":[93],"systems":[94],"that":[95,122],"do":[96],"not":[97],"possess":[98],"normalized":[99],"generating":[100],"analytical":[103],"form,":[104],"including":[105],"Legendre,":[107],"generalized":[108],"Laguerre,":[109],"Gegenbauer":[111],"families.":[112],"New":[113],"bounds":[114],"derived":[116],"$L_p(T)$":[120],"space":[121],"simultaneously":[123],"account":[124],"resulting":[131],"criteria":[132],"provide":[133],"guidance":[135],"selecting":[137],"number":[139],"terms":[142],"required":[143],"achieve":[145],"prescribed":[146],"levels":[147],"across":[152],"broader":[154],"class":[155],"polynomial-based":[157],"stochastic":[158],"process":[159],"models.":[160]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-02-07T00:00:00"}