{"id":"https://openalex.org/W2972070997","doi":null,"title":"Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series","display_name":"Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series","publication_year":2018,"publication_date":"2018-01-03","ids":{"openalex":"https://openalex.org/W2972070997","mag":"2972070997"},"language":"en","primary_location":{"id":"mag:2972070997","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.01079.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},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.01079.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031844627","display_name":"Dmitriy Feliksovich Kuznetsov","orcid":"https://orcid.org/0000-0001-5747-1282","observed_orcids":["https://orcid.org/0000-0001-5747-1282"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dmitriy F. Kuznetsov","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5747-1282","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5031844627"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.9258000254631042,"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":0.9258000254631042,"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/T11416","display_name":"Numerical methods for differential equations","score":0.06080000102519989,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.002300000051036477,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-multiple-fourier-series","display_name":"generalized multiple Fourier series","score":0.9300000071525574},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"mean squared error","score":0.9100000262260437},{"id":"https://openalex.org/keywords/mean-square-approximation","display_name":"mean-square approximation","score":0.7549999952316284},{"id":"https://openalex.org/keywords/fourier-legendre-series","display_name":"Fourier-Legendre series","score":0.968999981880188},{"id":"https://openalex.org/keywords/trigonometric-fourier-series","display_name":"trigonometric Fourier series","score":0.9789999723434448},{"id":"https://openalex.org/keywords/stratonovich-stochastic-integrals","display_name":"Stratonovich stochastic integrals","score":0.9160000085830688},{"id":"https://openalex.org/keywords/ito-stochastic-differential-equations","display_name":"It\u00f4 stochastic differential equations","score":0.8370000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7782981395721436},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6572239398956299},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6147292256355286},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6075074076652527},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4881182610988617},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44819843769073486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.418578565120697},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2972070997","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.01079.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}],"best_oa_location":{"id":"mag:2972070997","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.01079.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},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W194549626","https://openalex.org/W1489671651","https://openalex.org/W1575104486","https://openalex.org/W1587029759","https://openalex.org/W2027566891","https://openalex.org/W2769395688","https://openalex.org/W2779113173","https://openalex.org/W2780011229","https://openalex.org/W2782166265","https://openalex.org/W2783669549","https://openalex.org/W2784633966","https://openalex.org/W2784844186","https://openalex.org/W2785659303","https://openalex.org/W2786530640","https://openalex.org/W2848688724","https://openalex.org/W2910441900","https://openalex.org/W2956071680","https://openalex.org/W2977688219","https://openalex.org/W2977698769","https://openalex.org/W2980851859","https://openalex.org/W2980991073","https://openalex.org/W2982761286","https://openalex.org/W2992509162","https://openalex.org/W3007961686","https://openalex.org/W3017089874","https://openalex.org/W3018283577","https://openalex.org/W3022612525","https://openalex.org/W3028171098","https://openalex.org/W3093170089","https://openalex.org/W3103683316","https://openalex.org/W3105847064","https://openalex.org/W3173040430"],"related_works":["https://openalex.org/W4290974320","https://openalex.org/W2782427549","https://openalex.org/W3102101666","https://openalex.org/W2780011229","https://openalex.org/W3028171098","https://openalex.org/W6903642112","https://openalex.org/W3103683316","https://openalex.org/W6903721464","https://openalex.org/W6960024572","https://openalex.org/W6904026868"],"abstract_inverted_index":{"The":[0,158],"article":[1,162],"is":[2,38,152],"devoted":[3],"to":[4,88,166],"the":[5,8,28,33,39,42,49,55,70,75,78,101,112,118,134,156,161,167,194],"developement":[6],"of":[7,10,15,30,41,58,60,65,77,92,94,117,120,122,136,147,160,197],"method":[9,119],"expansion":[11,73,121],"and":[12,51,140],"mean-square":[13,56,195],"approximation":[14,59,146],"iterated":[16,43,61,95,123,148],"Ito":[17,44,62,96,105,124,173],"stochastic":[18,45,63,71,97,106,125,150,174,182],"integrals":[19,64,126,151],"based":[20,127],"on":[21,128],"generalized":[22,129],"multiple":[23,130,137,141],"Fourier":[24,131,143],"series":[25,132,139],"converging":[26],"in":[27,32,74,155],"sense":[29],"norm":[31],"space":[34],"$L_2([t,":[35],"T]^k)$":[36],"($k$":[37],"multiplicity":[40,66],"integral).":[46],"We":[47],"obtain":[48],"exact":[50],"approximate":[52],"expressions":[53],"for":[54,104,133,172],"error":[57],"$k$":[67],"($k\\in\\mathbb{N}$)":[68],"from":[69],"Taylor-Ito":[72],"framework":[76],"mentioned":[79],"method.":[80],"As":[81],"a":[82],"result,":[83],"we":[84,110],"do":[85],"not":[86],"need":[87],"use":[89],"redundant":[90],"terms":[91],"expansions":[93],"integrals,":[98],"that":[99],"complicate":[100],"numerical":[102,170],"methods":[103,171],"differential":[107,175,184],"equations.":[108],"Moreover,":[109],"proved":[111],"convergence":[113],"with":[114,186,193],"propability":[115],"1":[116],"cases":[135],"Fourier-Legendre":[138],"trigonometric":[142],"series.":[144],"Mean-square":[145],"Stratonovich":[149],"also":[153],"considered":[154],"article.":[157],"results":[159],"can":[163],"be":[164],"applied":[165],"high-order":[168],"strong":[169],"equations":[176,185],"as":[177,179],"well":[178],"non-commutative":[180],"semilinear":[181],"partial":[183],"multiplicative":[187],"trace":[188],"class":[189],"noise":[190],"(in":[191],"accordance":[192],"criterion":[196],"convergence).":[198]},"counts_by_year":[{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":5}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-09-12T00:00:00"}