{"id":"https://openalex.org/W1982687195","doi":"https://doi.org/10.1090/s0025-5718-09-02250-9","title":"Solving parabolic stochastic partial differential equations via averaging over characteristics","display_name":"Solving parabolic stochastic partial differential equations via averaging over characteristics","publication_year":2009,"publication_date":"2009-03-06","ids":{"openalex":"https://openalex.org/W1982687195","doi":"https://doi.org/10.1090/s0025-5718-09-02250-9","mag":"1982687195"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-09-02250-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02250-9","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066964804","display_name":"Grigori N. Milstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. Milstein","raw_affiliation_strings":["Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia","Ural State University , Lenin Str. 51, 620083 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia","institution_ids":[]},{"raw_affiliation_string":"Ural State University , Lenin Str. 51, 620083 Ekaterinburg, Russia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081243775","display_name":"M. V. Tretyakov","orcid":"https://orcid.org/0000-0002-7929-9046"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"M. Tretyakov","raw_affiliation_strings":["Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066964804"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4632,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.85712498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"78","issue":"268","first_page":"2075","last_page":"2106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9984999895095825,"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":0.9984999895095825,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.982200026512146,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.961899995803833,"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":0.9009976387023926},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.75808185338974},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6100045442581177},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5878596901893616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.572237491607666},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5469385385513306},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5210913419723511},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.5005326271057129},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.49330511689186096},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.4605708420276642},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.446646511554718},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.4456885755062103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4236491918563843},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30428773164749146},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.15765783190727234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9009976387023926},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.75808185338974},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6100045442581177},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5878596901893616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.572237491607666},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5469385385513306},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5210913419723511},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.5005326271057129},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.49330511689186096},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.4605708420276642},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.446646511554718},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.4456885755062103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4236491918563843},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30428773164749146},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.15765783190727234},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/s0025-5718-09-02250-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02250-9","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.6483","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.6483","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/0000-000-00/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.160.1786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.1786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-268/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","raw_type":"text"},{"id":"pmh:oai:elar.urfu.ru:10995/73165","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=67649644310","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Of Computation","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:jah.su:record/274286","is_oa":false,"landing_page_url":"http://hdl.handle.net/10995/73165","pdf_url":null,"source":{"id":"https://openalex.org/S4306401523","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Of Computation","raw_type":"Article"},{"id":"pmh:oai:lra.le.ac.uk:2381/26937","is_oa":false,"landing_page_url":"http://hdl.handle.net/2381/26937","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-09-02250-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02250-9","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02250-9/S0025-5718-09-02250-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8137425596","display_name":null,"funder_award_id":"EP/D049792/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320276","display_name":"University of Leicester","ror":"https://ror.org/04h699437"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1982687195.pdf","grobid_xml":"https://content.openalex.org/works/W1982687195.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W142776152","https://openalex.org/W194549626","https://openalex.org/W331237973","https://openalex.org/W335971307","https://openalex.org/W406087279","https://openalex.org/W1486164486","https://openalex.org/W1542004730","https://openalex.org/W1554532768","https://openalex.org/W1585178936","https://openalex.org/W1587029759","https://openalex.org/W1754812219","https://openalex.org/W1963921091","https://openalex.org/W1978697444","https://openalex.org/W1996322574","https://openalex.org/W2003393668","https://openalex.org/W2023088894","https://openalex.org/W2024999953","https://openalex.org/W2032894334","https://openalex.org/W2036234630","https://openalex.org/W2047312539","https://openalex.org/W2052082103","https://openalex.org/W2052849518","https://openalex.org/W2057105675","https://openalex.org/W2062147218","https://openalex.org/W2063999201","https://openalex.org/W2064200597","https://openalex.org/W2077089662","https://openalex.org/W2077802959","https://openalex.org/W2084865958","https://openalex.org/W2087895654","https://openalex.org/W2146636127","https://openalex.org/W2314913127","https://openalex.org/W2495773218","https://openalex.org/W2501086999","https://openalex.org/W2506877196","https://openalex.org/W2526191192","https://openalex.org/W2952415144","https://openalex.org/W3099415466","https://openalex.org/W4229844634","https://openalex.org/W4235700272","https://openalex.org/W4300475775","https://openalex.org/W6611532065"],"related_works":["https://openalex.org/W2006263304","https://openalex.org/W3020098708","https://openalex.org/W2357676173","https://openalex.org/W2155548976","https://openalex.org/W3147000368","https://openalex.org/W3023046551","https://openalex.org/W4235225734","https://openalex.org/W184885699","https://openalex.org/W2220638984","https://openalex.org/W4388215349"],"abstract_inverted_index":{"The":[0,84],"method":[1],"of":[2,15,41,51],"characteristics":[3],"(the":[4],"averaging":[5],"over":[6],"the":[7,11,22,44,49,62,78],"characteristic":[8],"formula)":[9],"and":[10,47,72,77],"weak-sense":[12],"numerical":[13,30,90],"integration":[14],"ordinary":[16],"stochastic":[17,34],"differential":[18,36],"equations":[19,37],"together":[20],"with":[21],"Monte":[23,63],"Carlo":[24,64],"technique":[25,60],"are":[26,55,75,82],"used":[27],"to":[28],"propose":[29],"methods":[31,69],"for":[32,61,70],"linear":[33,71],"partial":[35],"(SPDEs).":[38],"Their":[39],"orders":[40],"convergence":[42,54,80],"in":[43,48],"mean-square":[45],"sense":[46,50],"almost":[52],"sure":[53],"obtained.":[56],"A":[57],"variance":[58],"reduction":[59],"procedures":[65],"is":[66,87],"considered.":[67],"Layer":[68],"semilinear":[73],"SPDEs":[74],"constructed":[76],"corresponding":[79],"theorems":[81],"proved.":[83],"approach":[85],"developed":[86],"supported":[88],"by":[89],"experiments.":[91]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}