{"id":"https://openalex.org/W2030456910","doi":"https://doi.org/10.1137/090771843","title":"Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations","display_name":"Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2030456910","doi":"https://doi.org/10.1137/090771843","mag":"2030456910"},"language":"en","primary_location":{"id":"doi:10.1137/090771843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771843","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":"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/A5062566738","display_name":"Evelyn Buckwar","orcid":"https://orcid.org/0000-0002-6441-2990"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Evelyn Buckwar","raw_affiliation_strings":["E.Buckwar@hw.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"E.Buckwar@hw.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030280787","display_name":"C\u00f3nall Kelly","orcid":"https://orcid.org/0000-0002-9707-2822"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C\u00f3nall Kelly","raw_affiliation_strings":["conall.kelly@uwimona.edu.jm#TAB#"],"affiliations":[{"raw_affiliation_string":"conall.kelly@uwimona.edu.jm#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062566738"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.143,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.98253479,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"48","issue":"1","first_page":"298","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9689000248908997,"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/T11720","display_name":"Probability and Risk Models","score":0.9405999779701233,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8480943441390991},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6828924417495728},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6093023419380188},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5943498611450195},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5807658433914185},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5424533486366272},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5347890257835388},{"id":"https://openalex.org/keywords/linear-stability","display_name":"Linear stability","score":0.4928300678730011},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4772105813026428},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4529598355293274},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.45014503598213196},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.43896180391311646},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4377462863922119},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4337235689163208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3014478087425232},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.2876703143119812},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19657984375953674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10642263293266296}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8480943441390991},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6828924417495728},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6093023419380188},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5943498611450195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5807658433914185},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5424533486366272},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5347890257835388},{"id":"https://openalex.org/C43466630","wikidata":"https://www.wikidata.org/wiki/Q17098945","display_name":"Linear stability","level":3,"score":0.4928300678730011},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4772105813026428},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4529598355293274},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.45014503598213196},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.43896180391311646},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4377462863922119},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4337235689163208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3014478087425232},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.2876703143119812},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19657984375953674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10642263293266296},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090771843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771843","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1275718198","https://openalex.org/W1964221133","https://openalex.org/W1975417422","https://openalex.org/W1981663184","https://openalex.org/W2004828755","https://openalex.org/W2009391524","https://openalex.org/W2028796896","https://openalex.org/W2032759951","https://openalex.org/W2041274877","https://openalex.org/W2055122108","https://openalex.org/W2061342312","https://openalex.org/W2064645795","https://openalex.org/W2098533238","https://openalex.org/W2134799554","https://openalex.org/W2144375835","https://openalex.org/W2147247957","https://openalex.org/W2158710666","https://openalex.org/W2610857016","https://openalex.org/W3098347634"],"related_works":["https://openalex.org/W2071837188","https://openalex.org/W4245390618","https://openalex.org/W3022577984","https://openalex.org/W2081529693","https://openalex.org/W2087959462","https://openalex.org/W1993230404","https://openalex.org/W2023917379","https://openalex.org/W2018003366","https://openalex.org/W4206668610","https://openalex.org/W1970784083"],"abstract_inverted_index":{"We":[0,59,87],"develop":[1],"two":[2],"classes":[3],"of":[4,12,18,23,31,43,48,67,83,91,97,99,110,123],"test":[5,37,74,85,114],"equations":[6,22,38],"for":[7,94],"the":[8,29,68,84,89,95,100,130],"linear":[9,64],"stability":[10,65,82],"analysis":[11,54,66],"numerical":[13,105],"methods":[14],"applied":[15,71],"to":[16,53,72,107,113,129],"systems":[17,47,115],"stochastic":[19,32,44],"ordinary":[20],"differential":[21],"It\u00f4":[24],"type":[25],"(SODEs).":[26],"Motivated":[27],"by":[28],"theory":[30],"stabilization":[33],"and":[34,56,78,103],"destabilization,":[35],"these":[36,73],"capture":[39],"certain":[40],"fundamental":[41],"effects":[42],"perturbation":[45],"in":[46],"SODEs,":[49],"while":[50],"remaining":[51],"amenable":[52],"before":[55],"after":[57],"discretization.":[58],"then":[60],"carry":[61],"out":[62],"a":[63],"$\\theta$-Maruyama":[69,101],"method":[70,102],"equations,":[75],"investigating":[76],"mean-square":[77],"almost":[79],"sure":[80],"asymptotic":[81],"equilibria.":[86],"discuss":[88],"implications":[90],"our":[92,111],"work":[93],"notion":[96],"A-stability":[98],"use":[104],"simulation":[106],"suggest":[108],"extensions":[109],"results":[112],"with":[116],"nonnormal":[117],"drift":[118],"coefficients.":[119],"(A":[120],"corrected":[121],"version":[122],"this":[124],"paper":[125],"has":[126],"been":[127],"appended":[128],"originally":[131],"posted":[132],"pdf.)":[133]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
