{"id":"https://openalex.org/W2415356710","doi":"https://doi.org/10.1137/16m107801x","title":"Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming","display_name":"Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2415356710","doi":"https://doi.org/10.1137/16m107801x","mag":"2415356710"},"language":"en","primary_location":{"id":"doi:10.1137/16m107801x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m107801x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M107801X","source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M107801X","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071945495","display_name":"Juan Kuntz","orcid":"https://orcid.org/0000-0002-5855-6074"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Juan Kuntz","raw_affiliation_strings":["Department of Mathematics and Department of Bioengineering, Imperial College London, London, SW7 2AZ,UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Bioengineering, Imperial College London, London, SW7 2AZ,UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002796692","display_name":"Michela Ottobre","orcid":"https://orcid.org/0000-0002-8725-4278"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michela Ottobre","raw_affiliation_strings":["Mathematics Department, Heriot Watt University, Edinburgh, EH14 4AS, UK"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Heriot Watt University, Edinburgh, EH14 4AS, UK","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086007559","display_name":"Guy\u2010Bart Stan","orcid":"https://orcid.org/0000-0002-5560-902X"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Guy-Bart Stan","raw_affiliation_strings":["Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058010593","display_name":"Mauricio Barahona","orcid":"https://orcid.org/0000-0002-1089-5675"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mauricio Barahona","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London, SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071945495"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":{"value":2728,"currency":"EUR","value_usd":2942},"fwci":2.6446,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91482948,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"6","first_page":"A3891","last_page":"A3920"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9972000122070312,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8938323259353638},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7267946600914001},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6058452725410461},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5983646512031555},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.5889650583267212},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49046584963798523},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4660077691078186},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4409046173095703},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4291006326675415},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3515997529029846},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2931886315345764},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1534748077392578},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.12696075439453125},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.10679623484611511}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8938323259353638},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7267946600914001},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6058452725410461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5983646512031555},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.5889650583267212},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49046584963798523},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4660077691078186},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4409046173095703},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4291006326675415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3515997529029846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2931886315345764},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1534748077392578},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.12696075439453125},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.10679623484611511},{"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":3,"locations":[{"id":"doi:10.1137/16m107801x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m107801x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M107801X","source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.01153","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.01153","pdf_url":"https://arxiv.org/pdf/1606.01153","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":"pmh:oai:spiral.imperial.ac.uk:10044/1/41170","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/41170","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"A3920","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1137/16m107801x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m107801x","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M107801X","source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1511075568","display_name":null,"funder_award_id":"EP/M002187/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1899910","display_name":"Engineering Fellowships for Growth: Systems and control engineering framework for robust and efficient synthetic biology","funder_award_id":"EP/M002187/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2453345397","display_name":null,"funder_award_id":"EP/N014529/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G338695418","display_name":"Doctoral Training Grant","funder_award_id":"BB/F017510/1","funder_id":"https://openalex.org/F4320334629","funder_display_name":"Biotechnology and Biological Sciences Research Council"},{"id":"https://openalex.org/G4248603908","display_name":"Control Engineering Inspired Design Tools for Synthetic Biology","funder_award_id":"EP/I032223/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G439372692","display_name":null,"funder_award_id":"EP/I032223/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4984007400","display_name":"Multi-scale Dynamical Community Detection for the Digital Economy: from analyzing to influencing policy through Open Government data","funder_award_id":"EP/I017267/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5946492841","display_name":null,"funder_award_id":"EP/I017267/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7417950124","display_name":"EPSRC Centre for Mathematics of Precision Healthcare","funder_award_id":"EP/N014529/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334629","display_name":"Biotechnology and Biological Sciences Research Council","ror":"https://ror.org/00cwqg982"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2415356710.pdf","grobid_xml":"https://content.openalex.org/works/W2415356710.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W40754891","https://openalex.org/W49259755","https://openalex.org/W261814290","https://openalex.org/W1493070044","https://openalex.org/W1507296508","https://openalex.org/W1559197676","https://openalex.org/W1575104486","https://openalex.org/W1578233523","https://openalex.org/W1579485993","https://openalex.org/W1964730816","https://openalex.org/W1967184028","https://openalex.org/W1977569390","https://openalex.org/W1979011691","https://openalex.org/W1983452151","https://openalex.org/W1988093952","https://openalex.org/W1999913571","https://openalex.org/W2005424012","https://openalex.org/W2016745395","https://openalex.org/W2017032949","https://openalex.org/W2017170340","https://openalex.org/W2020032007","https://openalex.org/W2021268474","https://openalex.org/W2021290840","https://openalex.org/W2021784378","https://openalex.org/W2032411839","https://openalex.org/W2043747820","https://openalex.org/W2044108878","https://openalex.org/W2053199928","https://openalex.org/W2057152026","https://openalex.org/W2058496561","https://openalex.org/W2063665381","https://openalex.org/W2079184994","https://openalex.org/W2080510909","https://openalex.org/W2081624902","https://openalex.org/W2083746174","https://openalex.org/W2089644112","https://openalex.org/W2090967418","https://openalex.org/W2098613108","https://openalex.org/W2104049095","https://openalex.org/W2109246257","https://openalex.org/W2133404041","https://openalex.org/W2134489088","https://openalex.org/W2139346833","https://openalex.org/W2149498546","https://openalex.org/W2158840866","https://openalex.org/W2165281529","https://openalex.org/W2321772449","https://openalex.org/W4210379104","https://openalex.org/W4210545817","https://openalex.org/W4211165101","https://openalex.org/W4231021340","https://openalex.org/W4234542611","https://openalex.org/W4250135808","https://openalex.org/W4285719527","https://openalex.org/W4292027056","https://openalex.org/W4297748063"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2386048074","https://openalex.org/W2572095861"],"abstract_inverted_index":{"We":[0,74],"introduce":[1],"an":[2,38],"algorithm":[3],"based":[4],"on":[5,19],"semidefinite":[6,59],"programming":[7],"that":[8,113],"yields":[9],"increasing":[10],"(resp.,":[11,16],"decreasing)":[12],"sequences":[13],"of":[14,23,45,50,67,71,78,90,93,122,125,135,144],"lower":[15],"upper)":[17],"bounds":[18,33,115],"polynomial":[20,26],"stationary":[21,43,69,126],"averages":[22,127],"diffusions":[24],"with":[25,132],"drift":[27],"vector":[28],"and":[29,58,103,120,139],"diffusion":[30],"coefficients.":[31],"The":[32],"are":[34,62],"obtained":[35],"by":[36,41,54,64,99],"optimizing":[37],"objective,":[39],"determined":[40],"the":[42,48,65,72,76,79,88,114,118,123,133,136],"average":[44],"interest,":[46],"over":[47],"set":[49,124],"real":[51],"vectors":[52],"defined":[53],"certain":[55,129],"linear":[56,94],"equalities":[57],"inequalities":[60],"which":[61],"satisfied":[63],"moments":[66],"any":[68],"measure":[70],"diffusion.":[73],"exemplify":[75],"use":[77],"approach":[80],"through":[81],"several":[82],"applications:":[83],"a":[84,104],"Bayesian":[85],"inference":[86],"problem;":[87],"computation":[89,134],"Lyapunov":[91,137],"exponents":[92],"ordinary":[95],"differential":[96],"equations":[97],"perturbed":[98],"multiplicative":[100],"white":[101],"noise;":[102],"reliability":[105],"problem":[106],"from":[107],"structural":[108],"mechanics.":[109],"Additionally,":[110],"we":[111,140],"prove":[112],"converge":[116],"to":[117],"infimum":[119],"supremum":[121],"for":[128],"SDEs":[130],"associated":[131],"exponents,":[138],"provide":[141],"numerical":[142],"evidence":[143],"convergence":[145],"in":[146],"more":[147],"general":[148],"settings.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
