{"id":"https://openalex.org/W2053467044","doi":"https://doi.org/10.1137/s0040585x97982499","title":"Symmetric Integrals and Stochastic Analysis","display_name":"Symmetric Integrals and Stochastic Analysis","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2053467044","doi":"https://doi.org/10.1137/s0040585x97982499","mag":"2053467044"},"language":"en","primary_location":{"id":"doi:10.1137/s0040585x97982499","doi":"https://doi.org/10.1137/s0040585x97982499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0040585x97982499","pdf_url":null,"source":{"id":"https://openalex.org/S177771411","display_name":"Theory of Probability and Its Applications","issn_l":"0040-585X","issn":["0040-585X","1095-7219"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Theory of Probability & Its Applications","raw_type":"journal-article"},"volume":null,"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/A5073701722","display_name":"\u0424\u0430\u0440\u0438\u0442 \u0421\u0430\u0433\u0438\u0442\u043e\u0432\u0438\u0447 \u041d\u0430\u0441\u044b\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0002-6566-5156","observed_orcids":["https://orcid.org/0000-0002-6566-5156"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. S. Nasyrov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5073701722"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.27382402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"51","issue":"3","first_page":"486","last_page":"503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9794999957084656,"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":0.9794999957084656,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.004000000189989805,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/stieltjes-integral","display_name":"Stieltjes integral","score":0.9039999842643738},{"id":"https://openalex.org/keywords/stratonovich-stochastic-integrals","display_name":"Stratonovich stochastic integrals","score":0.9010000228881836},{"id":"https://openalex.org/keywords/ito-stochastic-differential-equations","display_name":"It\u00f4 stochastic differential equations","score":0.878000020980835},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.703000009059906},{"id":"https://openalex.org/keywords/improper-integrals","display_name":"improper integrals","score":0.8859999775886536},{"id":"https://openalex.org/keywords/continuous-functions","display_name":"continuous functions","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8926321268081665},{"id":"https://openalex.org/C90657474","wikidata":"https://www.wikidata.org/wiki/Q7622233","display_name":"Stratonovich integral","level":5,"score":0.7726186513900757},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6570149064064026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.556917130947113},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.527704656124115},{"id":"https://openalex.org/C54865166","wikidata":"https://www.wikidata.org/wiki/Q844937","display_name":"Multiple integral","level":2,"score":0.4944496154785156},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.492274671792984},{"id":"https://openalex.org/C2987636958","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic integral","level":3,"score":0.4551827609539032},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.451569527387619},{"id":"https://openalex.org/C38582570","wikidata":"https://www.wikidata.org/wiki/Q3825182","display_name":"Order of integration (calculus)","level":2,"score":0.4442934989929199},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4278866946697235},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.4271533191204071},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.4117797017097473},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38300153613090515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3479000926017761},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.29188793897628784},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.2429577112197876},{"id":"https://openalex.org/C41833934","wikidata":"https://www.wikidata.org/wiki/Q697181","display_name":"Riemann integral","level":4,"score":0.1509833037853241},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0040585x97982499","doi":"https://doi.org/10.1137/s0040585x97982499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0040585x97982499","pdf_url":null,"source":{"id":"https://openalex.org/S177771411","display_name":"Theory of Probability and Its Applications","issn_l":"0040-585X","issn":["0040-585X","1095-7219"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Theory of Probability & Its Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1987622062","https://openalex.org/W2011073103","https://openalex.org/W2074366794","https://openalex.org/W2085381800","https://openalex.org/W2971015701","https://openalex.org/W4244823317"],"related_works":["https://openalex.org/W4388514943","https://openalex.org/W2509209495","https://openalex.org/W1997940981","https://openalex.org/W4289104472","https://openalex.org/W3121388109","https://openalex.org/W4233813535","https://openalex.org/W1996962684","https://openalex.org/W2905812831","https://openalex.org/W2985826454","https://openalex.org/W1599518484"],"abstract_inverted_index":{"Symmetric":[0],"integrals":[1,20,69],"of":[2,16,29,33,51,54],"the":[3,17,27],"Stieltjes":[4],"type":[5],"for":[6],"an":[7],"arbitrary":[8],"continuous":[9],"function":[10],"and":[11,41,70],"which":[12,64],"are":[13,21],"determinate":[14],"versions":[15],"Stratonovich":[18],"stochastic":[19,34,43],"defined.":[22],"It":[23],"is":[24,46,65,73],"shown":[25],"that":[26],"solution":[28,50],"a":[30,38,49,52],"pathwise":[31],"analogue":[32],"differential":[35,44,56],"equations":[36,45],"with":[37],"symmetric":[39,62,68],"integral":[40],"It\u00f4":[42],"reduced":[47],"to":[48,67],"system":[53],"ordinary":[55],"equations.":[57],"The":[58],"relation":[59],"between":[60],"improper":[61],"integrals,":[63,72],"extended":[66],"Hellinger":[71],"established.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}