{"id":"https://openalex.org/W2338887853","doi":"https://doi.org/10.1137/16m1076654","title":"A Partial Fourier Transform Method for a Class of Hypoelliptic Kolmogorov Equations","display_name":"A Partial Fourier Transform Method for a Class of Hypoelliptic Kolmogorov Equations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2338887853","doi":"https://doi.org/10.1137/16m1076654","mag":"2338887853"},"language":"en","primary_location":{"id":"doi:10.1137/16m1076654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1076654","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1604.05268","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013285444","display_name":"Christoph Reisinger","orcid":"https://orcid.org/0000-0003-4027-5298"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christoph Reisinger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067836960","display_name":"Alan Whitley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan Whitley","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013285444"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00896599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"4","first_page":"1867","last_page":"1891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9987000226974487,"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":0.9987000226974487,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9925000071525574,"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"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypoelliptic-operator","display_name":"Hypoelliptic operator","score":0.9512344002723694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7469778656959534},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.653389573097229},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.5086656212806702},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.48789095878601074},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.46260058879852295},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45154261589050293},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.44349122047424316},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44096243381500244},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.42299243807792664},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4224076271057129},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3396926522254944},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.22157594561576843}],"concepts":[{"id":"https://openalex.org/C187123786","wikidata":"https://www.wikidata.org/wiki/Q4138816","display_name":"Hypoelliptic operator","level":4,"score":0.9512344002723694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7469778656959534},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.653389573097229},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.5086656212806702},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.48789095878601074},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.46260058879852295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45154261589050293},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.44349122047424316},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44096243381500244},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.42299243807792664},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4224076271057129},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3396926522254944},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.22157594561576843},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/16m1076654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1076654","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:oai:arXiv.org:1604.05268","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.05268","pdf_url":"https://arxiv.org/pdf/1604.05268","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:2338887853","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1604.05268.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:ora.ox.ac.uk:uuid:c7566244-56f7-4c60-821f-5471b739d5ae","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:c7566244-56f7-4c60-821f-5471b739d5ae","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.1604.05268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1604.05268","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1604.05268","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.05268","pdf_url":"https://arxiv.org/pdf/1604.05268","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2338887853.pdf","grobid_xml":"https://content.openalex.org/works/W2338887853.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W280536263","https://openalex.org/W1498051977","https://openalex.org/W1985543218","https://openalex.org/W1998527589","https://openalex.org/W2002021826","https://openalex.org/W2015666220","https://openalex.org/W2021268474","https://openalex.org/W2102591969","https://openalex.org/W2120516507","https://openalex.org/W2149272792","https://openalex.org/W2264204111","https://openalex.org/W2317502341","https://openalex.org/W2334164760","https://openalex.org/W2950476483"],"related_works":["https://openalex.org/W3145504892","https://openalex.org/W2538794260","https://openalex.org/W2951126530","https://openalex.org/W2894947447","https://openalex.org/W2246115504","https://openalex.org/W3017939622","https://openalex.org/W2952189940","https://openalex.org/W2248342625","https://openalex.org/W2017501040","https://openalex.org/W1209020212","https://openalex.org/W3195497641","https://openalex.org/W2966643436","https://openalex.org/W2133366645","https://openalex.org/W2955319763","https://openalex.org/W1971877693","https://openalex.org/W2980644941","https://openalex.org/W2902471570","https://openalex.org/W2281696564","https://openalex.org/W1487437180","https://openalex.org/W2083742115"],"abstract_inverted_index":{"We":[0,91,133,184],"consider":[1],"hypoelliptic":[2,71,145],"Kolmogorov":[3],"equations":[4],"in":[5,16,23,55,60,73,112,122,137,211],"$n+1$":[6],"spatial":[7,20,35,139],"dimensions,":[8],"with":[9,30,168,182],"$n\\geq":[10],"1$,":[11],"where":[12,96],"the":[13,17,24,33,37,51,56,61,76,94,97,102,113,123,130,138,143,161,193,199,205,216,219],"differential":[14,53],"operator":[15],"first":[18,57,103],"$n$":[19,58,104],"variables":[21,125],"featuring":[22],"equation":[25,38,146],"is":[26,46,80],"second-order":[27,135],"elliptic,":[28],"and":[29,45,59,75,116,173,178],"respect":[31],"to":[32,160,207],"$(n+1)$st":[34,62],"variable":[36,115],"contains":[39],"a":[40,84,109,208,223],"pure":[41],"transport":[42],"term":[43],"only":[44,100],"therefore":[47],"first-order":[48],"hyperbolic.":[49],"If":[50],"two":[52],"operators,":[54],"co-ordinate":[63],"directions,":[64],"do":[65],"not":[66],"commute,":[67],"we":[68,203],"benefit":[69],"from":[70],"regularization":[72],"time,":[74],"solution":[77],"for":[78,83,129,142,179],"$t>0$":[79],"smooth":[81],"even":[82],"Dirac":[85],"initial":[86,162],"datum":[87],"prescribed":[88],"at":[89],"$t=0$.":[90],"study":[92],"specifically":[93],"case":[95],"coefficients":[98],"depend":[99],"on":[101,198],"variables.":[105],"In":[106],"that":[107],"case,":[108],"Fourier":[110,195],"transform":[111,196],"last":[114],"standard":[117],"central":[118],"finite":[119],"difference":[120],"approximation":[121,191],"other":[124],"can":[126],"be":[127],"applied":[128],"numerical":[131],"solution.":[132],"prove":[134],"convergence":[136,188],"mesh":[140],"size":[141],"model":[144],"$\\frac{\\partial":[147],"u}{\\partial":[148,153,157],"t}":[149],"+":[150],"x":[151],"\\frac{\\partial":[152],"y}":[154],"=":[155,165],"\\frac{\\partial^2":[156],"x^2}$":[158],"subject":[159],"condition":[163],"$u(x,y,0)":[164],"\u03b4(x)":[166],"\u03b4(y)$,":[167],"$(x,y)":[169],"\\in":[170],"\\mathbb{R}":[171],"\\times\\mathbb{R}$":[172],"$t>0$,":[174],"proposed":[175],"by":[176],"Kolmogorov,":[177],"an":[180,190],"extension":[181],"$n=2$.":[183],"also":[185],"demonstrate":[186],"exponential":[187],"of":[189,192,218],"inverse":[194],"based":[197],"trapezium":[200],"rule.":[201],"Lastly,":[202],"apply":[204],"method":[206],"PDE":[209],"arising":[210],"mathematical":[212],"finance,":[213],"which":[214],"models":[215],"distribution":[217],"hedging":[220],"error":[221],"under":[222],"mis-specified":[224],"derivative":[225],"pricing":[226],"model.":[227]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}