{"id":"https://openalex.org/W2112859637","doi":"https://doi.org/10.1109/tit.1978.1055857","title":"Modeling and analysis of stochastic differential equations driven by point processes","display_name":"Modeling and analysis of stochastic differential equations driven by point processes","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W2112859637","doi":"https://doi.org/10.1109/tit.1978.1055857","mag":"2112859637"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1978.1055857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055857","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5013807415","display_name":"Steven I. Marcus","orcid":"https://orcid.org/0000-0002-4926-9567"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Marcus","raw_affiliation_strings":["Department of Electrical Engineering, University of Technology, Austin, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Technology, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013807415"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":6.9804,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.96864322,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"2","first_page":"164","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.8665000200271606,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.8665000200271606,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.7767000198364258,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6864114999771118},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6088781952857971},{"id":"https://openalex.org/keywords/stochastic-calculus","display_name":"Stochastic calculus","score":0.5966642498970032},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5066478848457336},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5054526329040527},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.4952341616153717},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4903428554534912},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4729868173599243},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4586932063102722},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.431282639503479},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.43040966987609863},{"id":"https://openalex.org/keywords/wiener-process","display_name":"Wiener process","score":0.42895203828811646},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.42409053444862366},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.42405790090560913},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.39615896344184875},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.3867548704147339},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34417712688446045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20050403475761414}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6864114999771118},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6088781952857971},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.5966642498970032},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5066478848457336},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5054526329040527},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.4952341616153717},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4903428554534912},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4729868173599243},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4586932063102722},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.431282639503479},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.43040966987609863},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.42895203828811646},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42409053444862366},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.42405790090560913},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.39615896344184875},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.3867548704147339},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34417712688446045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20050403475761414},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.0},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1978.1055857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055857","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320321368","display_name":"Hankyong National University","ror":"https://ror.org/0031nsg68"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W50201160","https://openalex.org/W63600139","https://openalex.org/W183133782","https://openalex.org/W1484406501","https://openalex.org/W1549258098","https://openalex.org/W1578776640","https://openalex.org/W1586568387","https://openalex.org/W1594932021","https://openalex.org/W1892810859","https://openalex.org/W1973376127","https://openalex.org/W1981252466","https://openalex.org/W2005711636","https://openalex.org/W2032006621","https://openalex.org/W2041277461","https://openalex.org/W2055108498","https://openalex.org/W2143588377","https://openalex.org/W2149707114","https://openalex.org/W2156635969","https://openalex.org/W2181351703","https://openalex.org/W2185883865","https://openalex.org/W2247038844","https://openalex.org/W2261974308","https://openalex.org/W2503996919","https://openalex.org/W2578416453","https://openalex.org/W4205756964","https://openalex.org/W4238721329","https://openalex.org/W4239002860","https://openalex.org/W4255034261","https://openalex.org/W4300810540","https://openalex.org/W6629045932","https://openalex.org/W6690676476"],"related_works":["https://openalex.org/W4226185373","https://openalex.org/W4237379163","https://openalex.org/W2950151144","https://openalex.org/W1580736543","https://openalex.org/W1560814075","https://openalex.org/W1559338696","https://openalex.org/W2045486080","https://openalex.org/W2060658157","https://openalex.org/W599760496","https://openalex.org/W2786718931"],"abstract_inverted_index":{"The":[0,18,110],"modeling":[1],"and":[2,30,127],"analysis":[3,97],"of":[4,21,88,95,98,112,120,133],"nonlinear":[5],"systems":[6,102,135],"described":[7],"by":[8,12,66,118],"differential":[9,28],"equations":[10,126],"driven":[11],"point":[13,51,78,105],"process":[14,52,79,106],"noise":[15,53,59,107,139],"are":[16,108,140],"considered.":[17],"stochastic":[19,72,131],"calculus":[20],"McShane":[22],"is":[23,36,39,80,116],"generalized":[24],"to":[25,76],"include":[26],"such":[27,61,99],"equations,":[29],"a":[31,70,77,92],"more":[32],"general":[33],"canonical":[34,43,114],"extension":[35,44,115],"defined.":[37],"It":[38],"proved":[40],"that":[41,54],"this":[42,82],"possesses":[45],"the":[46,58,86,96,113,121,130],"same":[47],"desirable":[48],"properties":[49],"for":[50,57,129],"it":[55],"does":[56],"processes,":[60],"as":[62],"Brownian":[63],"motion,":[64],"considered":[65],"McShane.":[67],"In":[68],"addition,":[69],"new":[71],"integral":[73,84],"with":[74,103,136],"respect":[75],"defined;":[81],"alternative":[83],"obeys":[85],"rules":[87],"ordinary":[89],"calculus.":[90],"As":[91],"special":[93],"case":[94],"systems,":[100],"linear":[101,134],"multiplicative":[104,137],"investigated.":[109],"consistency":[111],"studied":[117],"means":[119],"product":[122],"integral.":[123],"Finally,":[124],"moment":[125],"criteria":[128],"stability":[132],"Poisson":[138],"derived.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
