{"id":"https://openalex.org/W2130521152","doi":"https://doi.org/10.1287/moor.1090.0422","title":"Weak Differentiability of Product Measures","display_name":"Weak Differentiability of Product Measures","publication_year":2009,"publication_date":"2009-12-09","ids":{"openalex":"https://openalex.org/W2130521152","doi":"https://doi.org/10.1287/moor.1090.0422","mag":"2130521152"},"language":"en","primary_location":{"id":"doi:10.1287/moor.1090.0422","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.1090.0422","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.vu.nl/ws/files/2772884/weakdifferentiability.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069167370","display_name":"Bernd Heidergott","orcid":"https://orcid.org/0000-0002-3389-2311"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Bernd Heidergott","raw_affiliation_strings":["Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085220287","display_name":"Haralambie Leahu","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Haralambie Leahu","raw_affiliation_strings":["Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069167370"],"corresponding_institution_ids":["https://openalex.org/I865915315"],"apc_list":null,"apc_paid":null,"fwci":1.6664,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.85895033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"35","issue":"1","first_page":"27","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9940999746322632,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9897000193595886,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8113488554954529},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.715080201625824},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6368503570556641},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5969139337539673},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5753710865974426},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5027744770050049},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48513326048851013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45922747254371643},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4175504744052887},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3839092552661896},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34821125864982605},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3410707116127014},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.163852721452713},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14210310578346252},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1401379108428955},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08537018299102783}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8113488554954529},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.715080201625824},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6368503570556641},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5969139337539673},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5753710865974426},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5027744770050049},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48513326048851013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45922747254371643},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4175504744052887},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3839092552661896},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34821125864982605},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3410707116127014},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.163852721452713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14210310578346252},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1401379108428955},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08537018299102783},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1287/moor.1090.0422","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.1090.0422","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:publications/2a464d16-05df-44f0-9d7e-e602b4188b6b","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/2a464d16-05df-44f0-9d7e-e602b4188b6b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Heidergott, B F & Leahu, H 2010, 'Weak differentiability of product measures', Mathematics of Operations Research, vol. 35, no. 1, pp. 27-51. https://doi.org/10.1287/moor.1090.0422","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research.vu.nl:publications/f027d5a0-ac35-4b73-a866-65ea5ff15bf5","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/f027d5a0-ac35-4b73-a866-65ea5ff15bf5","pdf_url":"https://research.vu.nl/ws/files/2772884/weakdifferentiability.pdf","source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Heidergott, B F & Leahu, H 2010, 'Weak differentiability of product measures', Mathematics of Operations Research, vol. 35, pp. 27-51. https://doi.org/10.1287/moor.1090.0422","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:RePEc:inm:ormoor:v:35:y:2010:i:1:p:27-51","is_oa":false,"landing_page_url":"http://doi.org/10.1287/moor.1090.0422","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:dare.ubvu.vu.nl:1871/24214","is_oa":false,"landing_page_url":"http://hdl.handle.net/1871/24214","pdf_url":null,"source":{"id":"https://openalex.org/S4306400546","display_name":"Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"35","raw_type":"Article / Letter to editor"},{"id":"pmh:oai:library.tue.nl:658195","is_oa":false,"landing_page_url":"http://repository.tue.nl/658195","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0364-765X","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/2a464d16-05df-44f0-9d7e-e602b4188b6b","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/2a464d16-05df-44f0-9d7e-e602b4188b6b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Operations Research, 35(1), 27 - 51. INFORMS Institute for Operations Research and the Management Sciences","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:research.vu.nl:publications/f027d5a0-ac35-4b73-a866-65ea5ff15bf5","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/f027d5a0-ac35-4b73-a866-65ea5ff15bf5","pdf_url":"https://research.vu.nl/ws/files/2772884/weakdifferentiability.pdf","source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Heidergott, B F & Leahu, H 2010, 'Weak differentiability of product measures', Mathematics of Operations Research, vol. 35, pp. 27-51. https://doi.org/10.1287/moor.1090.0422","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"score":0.6399999856948853,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321014","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2130521152.pdf","grobid_xml":"https://content.openalex.org/works/W2130521152.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W8867774","https://openalex.org/W1178828506","https://openalex.org/W1547836095","https://openalex.org/W1550687824","https://openalex.org/W1579085115","https://openalex.org/W1594201577","https://openalex.org/W1795696915","https://openalex.org/W1970738610","https://openalex.org/W1975928280","https://openalex.org/W1982876709","https://openalex.org/W1991478799","https://openalex.org/W1995713768","https://openalex.org/W2010172006","https://openalex.org/W2043195713","https://openalex.org/W2064671882","https://openalex.org/W2079724820","https://openalex.org/W2089256099","https://openalex.org/W2095077541","https://openalex.org/W2097415784","https://openalex.org/W2108293203","https://openalex.org/W2109174772","https://openalex.org/W2109396699","https://openalex.org/W2115679377","https://openalex.org/W2121356029","https://openalex.org/W2168510061","https://openalex.org/W2168934542","https://openalex.org/W2311126677","https://openalex.org/W2315505061","https://openalex.org/W2321540280","https://openalex.org/W2595897327","https://openalex.org/W4241004244","https://openalex.org/W4246266336"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1980454230","https://openalex.org/W2300851791","https://openalex.org/W4318954848"],"abstract_inverted_index":{"In":[0,77,97],"this":[1,68],"paper,":[2],"we":[3],"study":[4],"cost":[5],"functions":[6],"over":[7],"a":[8,19,30,71,79,106],"finite":[9,94],"collection":[10],"of":[11,17,21,67,74,82,93,101,111,119,133],"random":[12],"variables.":[13],"For":[14],"these":[15],"types":[16],"models,":[18],"calculus":[20],"differentiation":[22],"is":[23,51,70,85],"developed":[24],"that":[25,87],"allows":[26,88],"us":[27],"to":[28,38,128,136,144],"obtain":[29],"closed-form":[31],"expression":[32],"for":[33,47,89,116,122],"derivatives":[34],"where":[35],"\u201cdifferentiation\u201d":[36],"has":[37],"be":[39,114],"understood":[40],"in":[41,149],"the":[42,49,102,117,124,129,137],"weak":[43,75,83],"sense.":[44],"The":[45,64],"technique":[46],"proving":[48],"results":[50],"new":[52],"and":[53,61,143],"establishes":[54],"an":[55],"interesting":[56],"link":[57],"between":[58],"functional":[59],"analysis":[60],"gradient":[62],"estimation.":[63],"key":[65],"contribution":[66],"paper":[69],"product":[72,80],"rule":[73,81],"differentiation.":[76],"addition,":[78],"analyticity":[84],"presented":[86],"Taylor":[90,125],"series":[91,126],"approximations":[92],"products":[95],"measures.":[96],"particular,":[98],"from":[99,140],"characteristics":[100],"individual":[103],"probability":[104],"measures,":[105],"lower":[107],"bound":[108],"(i.e.,":[109],"domain":[110],"convergence)":[112],"can":[113],"established":[115],"set":[118],"parameter":[120],"values":[121],"which":[123],"converges":[127],"true":[130],"value.":[131],"Applications":[132],"our":[134],"theory":[135],"ruin":[138],"problem":[139],"insurance":[141],"mathematics":[142],"stochastic":[145],"activity":[146],"networks":[147],"arising":[148],"project":[150],"evaluation":[151],"review":[152],"techniques":[153],"are":[154],"provided.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
