{"id":"https://openalex.org/W1939627962","doi":"https://doi.org/10.1109/tsp.2015.7296267","title":"The Milstein numerical scheme in solving stochastic second order networks","display_name":"The Milstein numerical scheme in solving stochastic second order networks","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1939627962","doi":"https://doi.org/10.1109/tsp.2015.7296267","mag":"1939627962"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.7296267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.7296267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 38th International Conference on Telecommunications and Signal Processing (TSP)","raw_type":"proceedings-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/A5071398004","display_name":"Edita Kol\u00e1\u0159ov\u00e1","orcid":"https://orcid.org/0000-0003-4992-627X"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Edita Kolarova","raw_affiliation_strings":["Department of Mathematics, Brno University of Technology, Brno, Czech Republic","Brno University of Technology, Department of Mathematics, Technick\u00e1 8, Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]},{"raw_affiliation_string":"Brno University of Technology, Department of Mathematics, Technick\u00e1 8, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000822834","display_name":"Lubom\u00edr Bran\u010d\u00edk","orcid":"https://orcid.org/0000-0001-9510-2058"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Lubomir Brancik","raw_affiliation_strings":["Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic","Brno University of Technology, Department of Radio Electronics, Technick\u00e1 12, Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]},{"raw_affiliation_string":"Brno University of Technology, Department of Radio Electronics, Technick\u00e1 12, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.05146223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"30","issue":null,"first_page":"276","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11444","display_name":"Electromagnetic Compatibility and Noise Suppression","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11444","display_name":"Electromagnetic Compatibility and Noise Suppression","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10787","display_name":"Lightning and Electromagnetic Phenomena","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9905999898910522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7507444620132446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5699370503425598},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.5493259429931641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5424633026123047},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5326124429702759},{"id":"https://openalex.org/keywords/stochastic-calculus","display_name":"Stochastic calculus","score":0.519710123538971},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.5056121349334717},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.44988304376602173},{"id":"https://openalex.org/keywords/stochastic-resonance","display_name":"Stochastic resonance","score":0.43931931257247925},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.43254342675209045},{"id":"https://openalex.org/keywords/rlc-circuit","display_name":"RLC circuit","score":0.4287532567977905},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4196423888206482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3954232335090637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36264467239379883},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33757174015045166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2449456751346588},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20150154829025269}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7507444620132446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5699370503425598},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.5493259429931641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5424633026123047},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5326124429702759},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.519710123538971},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.5056121349334717},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.44988304376602173},{"id":"https://openalex.org/C207658827","wikidata":"https://www.wikidata.org/wiki/Q1999781","display_name":"Stochastic resonance","level":4,"score":0.43931931257247925},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.43254342675209045},{"id":"https://openalex.org/C89880566","wikidata":"https://www.wikidata.org/wiki/Q323477","display_name":"RLC circuit","level":4,"score":0.4287532567977905},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4196423888206482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3954232335090637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36264467239379883},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33757174015045166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2449456751346588},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20150154829025269},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C52192207","wikidata":"https://www.wikidata.org/wiki/Q5322","display_name":"Capacitor","level":3,"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/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2015.7296267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.7296267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 38th International Conference on Telecommunications and Signal Processing (TSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W761008951","https://openalex.org/W1983097489","https://openalex.org/W1983507864","https://openalex.org/W2036819178","https://openalex.org/W2068515062","https://openalex.org/W2069301999","https://openalex.org/W2081347296","https://openalex.org/W2099579103","https://openalex.org/W2124894082","https://openalex.org/W2141436719","https://openalex.org/W2145667804","https://openalex.org/W2170316986","https://openalex.org/W2329869012","https://openalex.org/W2546505240","https://openalex.org/W2799664482","https://openalex.org/W4294990616"],"related_works":["https://openalex.org/W4226185373","https://openalex.org/W2060658157","https://openalex.org/W3165912934","https://openalex.org/W599760496","https://openalex.org/W1981477920","https://openalex.org/W3125773376","https://openalex.org/W2073895749","https://openalex.org/W17889898","https://openalex.org/W2078751837","https://openalex.org/W2786718931"],"abstract_inverted_index":{"The":[0],"paper":[1],"deals":[2],"with":[3,22],"vector":[4],"It\u00f4":[5,53],"stochastic":[6,24,39,48,64,83],"integral":[7],"equations.":[8],"We":[9,75],"replace":[10],"a":[11,23,28,45],"parameter":[12],"in":[13,85],"the":[14,18,32,38,42,52,63,68,71,79,82,86],"deterministic":[15],"model":[16,40],"of":[17,41,62,81],"RLC":[19],"electrical":[20],"circuit":[21,43],"one,":[25],"by":[26],"adding":[27],"noise":[29],"term":[30],"to":[31],"coefficient":[33],"and":[34,70],"so":[35],"we":[36,55,66],"introduce":[37],"as":[44],"second":[46],"order":[47],"differential":[49],"equation.":[50,58],"By":[51],"calculus":[54],"solve":[56],"this":[57],"For":[59],"numerical":[60,73],"simulations":[61],"trajectories":[65,84],"present":[67],"Euler":[69],"Milstein":[72],"schemes.":[74],"used":[76],"Matlab":[77],"for":[78],"computations":[80],"examples.":[87]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}