{"id":"https://openalex.org/W1965150518","doi":"https://doi.org/10.1137/s0036142999360275","title":"Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures","display_name":"Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1965150518","doi":"https://doi.org/10.1137/s0036142999360275","mag":"1965150518"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999360275","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999360275","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/A5051155796","display_name":"Erika Hausenblas","orcid":"https://orcid.org/0000-0002-1762-9521"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Erika Hausenblas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051155796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.63590185,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.76134867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":"1","first_page":"87","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9957000017166138,"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":0.9957000017166138,"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":0.9854000210762024,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8261983394622803},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6690183877944946},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.636893630027771},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5616961717605591},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.49982690811157227},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.4631703495979309},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46237656474113464},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.44856661558151245},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.44520774483680725},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.43832284212112427},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.41945773363113403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.362727552652359},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22556015849113464},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12497323751449585}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8261983394622803},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6690183877944946},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.636893630027771},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5616961717605591},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.49982690811157227},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.4631703495979309},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46237656474113464},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.44856661558151245},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.44520774483680725},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.43832284212112427},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.41945773363113403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.362727552652359},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22556015849113464},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12497323751449585},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142999360275","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999360275","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":12,"referenced_works":["https://openalex.org/W1583938685","https://openalex.org/W1969629931","https://openalex.org/W1983261215","https://openalex.org/W1996705901","https://openalex.org/W2037912907","https://openalex.org/W2077315519","https://openalex.org/W2099176186","https://openalex.org/W2163891345","https://openalex.org/W2997679055","https://openalex.org/W3027327446","https://openalex.org/W4205302168","https://openalex.org/W4300810540"],"related_works":["https://openalex.org/W2225046392","https://openalex.org/W1939724041","https://openalex.org/W4252323550","https://openalex.org/W2065735671","https://openalex.org/W4302594354","https://openalex.org/W2557614388","https://openalex.org/W2834438054","https://openalex.org/W4235306759","https://openalex.org/W1988309847","https://openalex.org/W2963985698"],"abstract_inverted_index":{"Let":[0],"Xt":[1],"be":[2,37],"the":[3,45,48,68,71,85,88,96],"solution":[4],"of":[5,24,47,70,100],"a":[6,17],"stochastic":[7],"differential":[8],"equation":[9],"(SDE)":[10],"with":[11],"starting":[12],"point":[13],"x0":[14],"driven":[15,57],"by":[16,39,58],"Poisson":[18],"random":[19],"measure.":[20],"Additive":[21],"functionals":[22],"are":[23,31],"interest":[25],"in":[26],"various":[27],"applications.":[28],"Nevertheless":[29],"they":[30],"often":[32],"unknown":[33],"and":[34],"can":[35],"only":[36],"found":[38],"simulation":[40],"on":[41,55],"computers.":[42],"We":[43],"investigate":[44],"quality":[46],"Euler":[49],"approximation.":[50],"Our":[51],"main":[52],"emphasis":[53],"is":[54,95],"SDEs":[56],"an":[59],"$\\alpha$-stable":[60],"process,":[61],"$0<\\alpha":[62],"<":[63],"2$,":[64],"where":[65,87,93],"we":[66,83],"study":[67],"approximation":[69],"Monte":[72],"Carlo":[73],"error":[74],"${\\Bbb":[75],"E}":[76],"[f(X_T)]$,":[77],"f":[78],"belonging":[79],"to":[80],"${L}^\\infty$.":[81],"Moreover,":[82],"treat":[84],"case":[86],"time":[89,99],"equals":[90],"$T\\wedge":[91],"\\tau$,":[92],"$\\tau$":[94],"first":[97],"exit":[98],"some":[101],"interval.":[102]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}