{"id":"https://openalex.org/W7223118488","doi":"https://doi.org/10.48550/arxiv.2610.28552","title":"Strong Convergence of Fully Discrete Tamed Euler Approximations for Time-Changed Stochastic Delay Differential Equations","display_name":"Strong Convergence of Fully Discrete Tamed Euler Approximations for Time-Changed Stochastic Delay Differential Equations","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223118488","doi":"https://doi.org/10.48550/arxiv.2610.28552"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28552","pdf_url":"https://arxiv.org/pdf/2610.28552","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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.28552","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092715299","display_name":"Ruchun Zuo","orcid":"https://orcid.org/0009-0008-9629-5072","observed_orcids":["https://orcid.org/0009-0008-9629-5072"]},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuo, Ruchun","raw_affiliation_strings":["Department of Mathematics , Shanghai Normal University Shanghai 200234 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shanghai Normal University Shanghai 200234 , China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159204689","display_name":"Qian Guo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo, Qian","raw_affiliation_strings":["Department of Mathematics , Shanghai Normal University Shanghai 200234 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shanghai Normal University Shanghai 200234 , China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.5170999765396118,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.5170999765396118,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.39820000529289246,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.020400000736117363,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/strong-convergence","display_name":"strong convergence","score":0.8970000147819519},{"id":"https://openalex.org/keywords/subordinating-conjunctions","display_name":"subordinating conjunctions","score":0.8309999704360962},{"id":"https://openalex.org/keywords/sampling-error","display_name":"sampling error","score":0.6399999856948853},{"id":"https://openalex.org/keywords/inverse-subordinator","display_name":"inverse subordinator","score":0.5680000185966492},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"multiplicative noise","score":0.7089999914169312}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468000292778015},{"id":"https://openalex.org/C2781362121","wikidata":"https://www.wikidata.org/wiki/Q7631785","display_name":"Subordinator","level":3,"score":0.7878999710083008},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6855000257492065},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6262999773025513},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5480999946594238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5291000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5073000192642212},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49390000104904175},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.46939998865127563},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43619999289512634},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.421999990940094},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.3580000102519989},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3499999940395355},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.32679998874664307},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28552","pdf_url":"https://arxiv.org/pdf/2610.28552","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.28552","doi":"https://doi.org/10.48550/arxiv.2610.28552","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28552","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28552","pdf_url":"https://arxiv.org/pdf/2610.28552","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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223118488.pdf","grobid_xml":"https://content.openalex.org/works/W7223118488.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W92521201","https://openalex.org/W1584770368","https://openalex.org/W1978275259","https://openalex.org/W1990932185","https://openalex.org/W1995522593","https://openalex.org/W2077252113","https://openalex.org/W2093124498","https://openalex.org/W2108823069","https://openalex.org/W2111271983","https://openalex.org/W2130253079","https://openalex.org/W2140333923","https://openalex.org/W2147688960","https://openalex.org/W2911324870","https://openalex.org/W2927309664","https://openalex.org/W2951662467","https://openalex.org/W2961197206","https://openalex.org/W2963263803","https://openalex.org/W2964241880","https://openalex.org/W3006192377","https://openalex.org/W3013740178","https://openalex.org/W3025554787","https://openalex.org/W3186851260","https://openalex.org/W4293092461","https://openalex.org/W4392812251","https://openalex.org/W4400229891","https://openalex.org/W4406306792","https://openalex.org/W4407319741","https://openalex.org/W4407836882","https://openalex.org/W4410843993","https://openalex.org/W4416615485","https://openalex.org/W7130385278","https://openalex.org/W7172221684","https://openalex.org/W7213906169","https://openalex.org/W7214055899"],"related_works":["https://openalex.org/W7213906169","https://openalex.org/W4323038270","https://openalex.org/W4417429763","https://openalex.org/W2735205919","https://openalex.org/W2574523910","https://openalex.org/W2153127252","https://openalex.org/W1545518728","https://openalex.org/W2105544306","https://openalex.org/W3000289125","https://openalex.org/W7164838981"],"abstract_inverted_index":{"We":[0],"establish":[1],"the":[2,30,43,71,76,88,92,99,108,123,147],"strong":[3,65,127],"convergence":[4,128,160],"of":[5,70,110,130,149],"a":[6,83,104,126,139,143],"fully":[7],"discrete":[8],"equidistant":[9],"tamed":[10],"Euler--Maruyama":[11],"(ETEM)":[12],"method":[13],"for":[14,56,138,153,161],"time-changed":[15],"stochastic":[16],"delay":[17,166,171],"differential":[18],"equations":[19,172],"(TCSDDEs)":[20],"with":[21,38,61,142,173],"state-dependent":[22],"$\\mathrm{d}t$":[23],"drifts.":[24],"A":[25,133],"coupled":[26],"one-sided":[27],"condition":[28],"on":[29],"subordinator-driven":[31],"drift":[32],"and":[33,45,75,94,120,163],"diffusion":[34],"allows":[35],"superlinear":[36,165],"coefficients":[37,114],"polynomial":[39,151],"growth":[40],"in":[41,68,116],"both":[42,117,150],"current":[44],"delayed":[46],"states.":[47],"For":[48,113],"subordinators":[49,97],"whose":[50],"Laplace":[51],"exponent":[52],"satisfies":[53],"$\u03c8(\u03bb)\\geq":[54],"c_1\u03bb^\u03b1$":[55],"all":[57],"sufficiently":[58],"large":[59],"$\u03bb$,":[60],"$\u03b1\\in(0,1)$,":[62],"we":[63],"derive":[64],"error":[66,101],"bounds":[67],"terms":[69],"time":[72,111,118,175],"step":[73,79],"$\u0394$":[74],"subordinator":[77,145],"sampling":[78,100],"$\u03b4$,":[80],"without":[81,102],"imposing":[82],"relationship":[84],"between":[85],"them.":[86],"Comparing":[87],"partitions":[89],"generated":[90],"by":[91],"exact":[93],"approximate":[95],"inverse":[96],"controls":[98],"introducing":[103],"factor":[105],"proportional":[106],"to":[107],"number":[109],"steps.":[112],"Lipschitz":[115,121],"arguments":[119],"history,":[122],"scheme":[124],"achieves":[125],"rate":[129],"order":[131],"$\u0394^{\u03b1/2}(1+|\\log\u0394|)^{(1-\u03b1)/2}+\\sqrt{\u03b4(1+|\\log\u03b4|)}$.":[132],"terminal":[134],"lower":[135],"bound":[136],"$c(\u0394^{\u03b1/2}+\u03b4^{1/2})$":[137],"multiplicative-noise":[140],"equation":[141],"stable":[144],"establishes":[146],"sharpness":[148],"exponents":[152],"this":[154],"Euler":[155],"scheme.":[156],"Numerical":[157],"experiments":[158],"illustrate":[159],"nonautonomous":[162],"multidimensional":[164],"equations,":[167],"as":[168,170],"well":[169],"low-regularity":[174],"dependence.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}