{"id":"https://openalex.org/W137264176","doi":"https://doi.org/10.1007/978-1-4612-3938-3_8","title":"Representation of Semimartingale Markov Processes in Terms of Wiener Processes and Poisson Random Measures","display_name":"Representation of Semimartingale Markov Processes in Terms of Wiener Processes and Poisson Random Measures","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W137264176","doi":"https://doi.org/10.1007/978-1-4612-3938-3_8","mag":"137264176"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4612-3938-3_8","doi":"https://doi.org/10.1007/978-1-4612-3938-3_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-3938-3_8","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Seminar on Stochastic Processes, 1981","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W1994958109","display_name":"Seminar on Stochastic Processes, 1981"},"type":"book-chapter","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/A5003505966","display_name":"Erhan \u00c7\u0131nlar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. \u00c7inlar","raw_affiliation_strings":["Northwestern University****"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwestern University****","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109281241","display_name":"Jean Jacod","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Jacod","raw_affiliation_strings":["IRISA, Lab. associ\u00e9 au CNRS, Universit\u00e9 de Rennes, Rennes Cedex, France","UNIVERSITE DE RENNES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRISA, Lab. associ\u00e9 au CNRS, Universit\u00e9 de Rennes, Rennes Cedex, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2802519937","https://openalex.org/I56067802"]},{"raw_affiliation_string":"UNIVERSITE DE RENNES","institution_ids":["https://openalex.org/I56067802"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.6528,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.96696697,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"159","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.8076000213623047,"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":0.8076000213623047,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.1462000012397766,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13500","display_name":"Probability and Statistical Research","score":0.01769999973475933,"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/hunt-processes","display_name":"Hunt processes","score":0.9750000238418579},{"id":"https://openalex.org/keywords/random-time-change","display_name":"random time change","score":0.7450000047683716},{"id":"https://openalex.org/keywords/stochastic-integral-equations","display_name":"stochastic integral equations","score":0.8560000061988831},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.8489999771118164},{"id":"https://openalex.org/keywords/poisson-random-measure","display_name":"Poisson random measure","score":0.9010000228881836}],"concepts":[{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.8754355311393738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7485183477401733},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5787041783332825},{"id":"https://openalex.org/C155051063","wikidata":"https://www.wikidata.org/wiki/Q1290919","display_name":"Cox process","level":4,"score":0.5474728345870972},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5025150775909424},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.498751163482666},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4929544925689697},{"id":"https://openalex.org/C163540672","wikidata":"https://www.wikidata.org/wiki/Q1115431","display_name":"Markov renewal process","level":5,"score":0.4794858396053314},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47619783878326416},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46748703718185425},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.46691182255744934},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.4323105216026306},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.43169718980789185},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.42397475242614746},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.4138685464859009},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.4131716787815094},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.36027801036834717},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30768683552742004},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2959098219871521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2659553289413452},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.24396082758903503},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.17792296409606934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1456020474433899},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11525076627731323},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4612-3938-3_8","doi":"https://doi.org/10.1007/978-1-4612-3938-3_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-3938-3_8","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Seminar on Stochastic Processes, 1981","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions","score":0.6800000071525574}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W80265126","https://openalex.org/W97254305","https://openalex.org/W1523471994","https://openalex.org/W1581147332","https://openalex.org/W1668826802","https://openalex.org/W1779951586","https://openalex.org/W1829270309","https://openalex.org/W1972121666","https://openalex.org/W1976200365","https://openalex.org/W1994933289","https://openalex.org/W1997204748","https://openalex.org/W1998107368","https://openalex.org/W2005846580","https://openalex.org/W2007700189","https://openalex.org/W2014529209","https://openalex.org/W2015431330","https://openalex.org/W2037912907","https://openalex.org/W2087848794","https://openalex.org/W2141216118","https://openalex.org/W2316933815","https://openalex.org/W2325448565","https://openalex.org/W2572955172","https://openalex.org/W2584345224","https://openalex.org/W3116819471","https://openalex.org/W4238476036","https://openalex.org/W4243892862","https://openalex.org/W6631490330","https://openalex.org/W6649722129","https://openalex.org/W6987788218","https://openalex.org/W6991922993"],"related_works":["https://openalex.org/W4372358147","https://openalex.org/W4285483632","https://openalex.org/W629086515","https://openalex.org/W1857434737","https://openalex.org/W2776439733","https://openalex.org/W4206727940","https://openalex.org/W56351099","https://openalex.org/W1987042712","https://openalex.org/W4298388735","https://openalex.org/W2037912907"],"abstract_inverted_index":{"Our":[0],"object":[1],"is":[2,22,28,70,107,125],"the":[3,56,64,68,77,92,130],"representation":[4,93],"of":[5,14,67,80,86,119,132],"Markov":[6,37,112],"processes":[7,16,82],"taking":[8],"values":[9],"in":[10,12,129],"IRm":[11],"terms":[13],"well-understood":[15],"and":[17,50,100],"operations.":[18],"The":[19],"major":[20],"result":[21],"that":[23,39,108],"every":[24,109],"semimartingale":[25],"Hunt":[26,81],"process":[27,38,49,69,113],"obtained":[29],"by":[30,46,72],"a":[31,36,41,47,51,96],"random":[32,53,98],"time":[33],"change":[34],"from":[35],"satisfies":[40],"stochastic":[42,57,102],"integral":[43],"equation":[44,58],"driven":[45],"Wiener":[48],"Poisson":[52,97],"measure.":[54],"If":[55],"has":[59],"no":[60,101],"other":[61],"solutions,":[62],"then":[63],"probability":[65],"law":[66],"specified":[71],"four":[73],"deterministic":[74,127],"functions.":[75],"In":[76],"particular":[78],"case":[79],"whose":[83,116],"paths":[84,117],"are":[85,118],"bounded":[87,120],"variation":[88,121],"over":[89,122],"finite":[90,123],"intervals,":[91],"involves":[94],"only":[95],"measure":[99],"integrals.":[103],"A":[104],"further":[105],"corollary":[106],"continuous":[110],"strong":[111],"on":[114],"IRm.":[115],"intervals":[124],"totally":[126],"except":[128],"choice":[131],"initial":[133],"state.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}
