{"id":"https://openalex.org/W2054125756","doi":"https://doi.org/10.1109/mesa.2014.6935520","title":"Self-similar stochastic models with stationary increments for symmetric space-time fractional diffusion","display_name":"Self-similar stochastic models with stationary increments for symmetric space-time fractional diffusion","publication_year":2014,"publication_date":"2014-09-01","ids":{"openalex":"https://openalex.org/W2054125756","doi":"https://doi.org/10.1109/mesa.2014.6935520","mag":"2054125756"},"language":"en","primary_location":{"id":"doi:10.1109/mesa.2014.6935520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mesa.2014.6935520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.11824/192","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015221131","display_name":"Gianni Pagnini","orcid":"https://orcid.org/0000-0001-9917-4614"},"institutions":[{"id":"https://openalex.org/I2802176441","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32","country_code":"ES","type":"education","lineage":["https://openalex.org/I2802176441"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Gianni Pagnini","raw_affiliation_strings":["BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain","BCAM \u2013 Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009, Bilbao, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain","institution_ids":["https://openalex.org/I2802176441"]},{"raw_affiliation_string":"BCAM \u2013 Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009, Bilbao, Spain","institution_ids":["https://openalex.org/I2802176441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015221131"],"corresponding_institution_ids":["https://openalex.org/I2802176441"],"apc_list":null,"apc_paid":null,"fwci":0.2465,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58470566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9822999835014343,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.7231936454772949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6641789674758911},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.6535731554031372},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5594956874847412},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.5579069256782532},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.5436127185821533},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.5317847728729248},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.502657413482666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48926350474357605},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.4704393744468689},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.463499516248703},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.451845645904541},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.42886072397232056},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4219207167625427},{"id":"https://openalex.org/keywords/ornstein\u2013uhlenbeck-process","display_name":"Ornstein\u2013Uhlenbeck process","score":0.4212946593761444},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.4104654788970947},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17983362078666687},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09093976020812988}],"concepts":[{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.7231936454772949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6641789674758911},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.6535731554031372},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5594956874847412},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5579069256782532},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.5436127185821533},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5317847728729248},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.502657413482666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48926350474357605},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4704393744468689},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.463499516248703},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.451845645904541},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.42886072397232056},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4219207167625427},{"id":"https://openalex.org/C31634936","wikidata":"https://www.wikidata.org/wiki/Q1757587","display_name":"Ornstein\u2013Uhlenbeck process","level":3,"score":0.4212946593761444},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.4104654788970947},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17983362078666687},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09093976020812988},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/mesa.2014.6935520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mesa.2014.6935520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA)","raw_type":"proceedings-article"},{"id":"pmh:oai:bird.bcamath.org:20.500.11824/192","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11824/192","pdf_url":null,"source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:bird.bcamath.org:20.500.11824/192","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11824/192","pdf_url":null,"source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1708820433","display_name":null,"funder_award_id":"BERC 2014-2017 program","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G3129058151","display_name":null,"funder_award_id":"BCAM Severo Ochoa accreditation SEV-2013-0323","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G3244436707","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320328444","funder_display_name":"Basque Center for Applied Mathematics"},{"id":"https://openalex.org/G3779338858","display_name":null,"funder_award_id":"2014-2017","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G4252991836","display_name":null,"funder_award_id":"BERC 2014-2017","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4373130462","display_name":null,"funder_award_id":"2013-0323","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5281057304","display_name":null,"funder_award_id":"2014-2017","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6939876626","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G7529331022","display_name":null,"funder_award_id":"BERC 2014-2017","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G8296132195","display_name":null,"funder_award_id":"SEV-2013-0323","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320328444","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":99,"referenced_works":["https://openalex.org/W16305314","https://openalex.org/W110340196","https://openalex.org/W146759740","https://openalex.org/W153317212","https://openalex.org/W203398882","https://openalex.org/W1527783838","https://openalex.org/W1633869013","https://openalex.org/W1681895783","https://openalex.org/W1732044815","https://openalex.org/W1821538050","https://openalex.org/W1964858852","https://openalex.org/W1966255698","https://openalex.org/W1966793822","https://openalex.org/W1973950856","https://openalex.org/W1974234252","https://openalex.org/W1974258811","https://openalex.org/W1977360274","https://openalex.org/W1981832301","https://openalex.org/W1996746155","https://openalex.org/W1997185714","https://openalex.org/W2000526322","https://openalex.org/W2002339544","https://openalex.org/W2004530012","https://openalex.org/W2005512948","https://openalex.org/W2006907269","https://openalex.org/W2013915547","https://openalex.org/W2016755336","https://openalex.org/W2018361434","https://openalex.org/W2018674686","https://openalex.org/W2023892618","https://openalex.org/W2023918785","https://openalex.org/W2026413941","https://openalex.org/W2027849256","https://openalex.org/W2030206514","https://openalex.org/W2030547991","https://openalex.org/W2030986556","https://openalex.org/W2033402214","https://openalex.org/W2034865749","https://openalex.org/W2035967427","https://openalex.org/W2037310801","https://openalex.org/W2039324033","https://openalex.org/W2040226882","https://openalex.org/W2040561350","https://openalex.org/W2045969550","https://openalex.org/W2046199332","https://openalex.org/W2046340221","https://openalex.org/W2046898218","https://openalex.org/W2056427269","https://openalex.org/W2064152110","https://openalex.org/W2064361774","https://openalex.org/W2065096983","https://openalex.org/W2065214339","https://openalex.org/W2066074538","https://openalex.org/W2071324059","https://openalex.org/W2075110582","https://openalex.org/W2078419687","https://openalex.org/W2086845657","https://openalex.org/W2087421943","https://openalex.org/W2090558929","https://openalex.org/W2091256898","https://openalex.org/W2093251311","https://openalex.org/W2094249280","https://openalex.org/W2094830203","https://openalex.org/W2102049346","https://openalex.org/W2105204676","https://openalex.org/W2119408320","https://openalex.org/W2131914906","https://openalex.org/W2134264301","https://openalex.org/W2136254520","https://openalex.org/W2142019556","https://openalex.org/W2147833506","https://openalex.org/W2150143762","https://openalex.org/W2153593393","https://openalex.org/W2155831782","https://openalex.org/W2157358771","https://openalex.org/W2158112438","https://openalex.org/W2159325467","https://openalex.org/W2164539400","https://openalex.org/W2169021824","https://openalex.org/W2476555123","https://openalex.org/W2787959293","https://openalex.org/W2790825170","https://openalex.org/W3098062605","https://openalex.org/W3099066240","https://openalex.org/W3099704509","https://openalex.org/W3099957218","https://openalex.org/W3102521085","https://openalex.org/W3103124906","https://openalex.org/W3105918404","https://openalex.org/W3125004152","https://openalex.org/W3212699936","https://openalex.org/W4229825750","https://openalex.org/W4244854774","https://openalex.org/W4250515647","https://openalex.org/W4285719527","https://openalex.org/W4297810857","https://openalex.org/W6606041292","https://openalex.org/W6636599831","https://openalex.org/W6683593063"],"related_works":["https://openalex.org/W2135603267","https://openalex.org/W2951335089","https://openalex.org/W3028286073","https://openalex.org/W1996593003","https://openalex.org/W2062052461","https://openalex.org/W2963787549","https://openalex.org/W1874491647","https://openalex.org/W4220773456","https://openalex.org/W3024364149","https://openalex.org/W3039142278"],"abstract_inverted_index":{"An":[0],"approach":[1,16],"to":[2,67,70,82,110],"develop":[3],"stochastic":[4,18,90],"models":[5],"for":[6,29,47],"studying":[7],"anomalous":[8],"diffusion":[9,79,122],"is":[10,21,33,92],"proposed.":[11],"In":[12],"particular,":[13],"in":[14,61,97],"this":[15,87],"the":[17,24,62,71,74,83,103,106,111,117,120,124],"particle":[19,48],"trajectory":[20],"based":[22],"on":[23],"fractional":[25,78,84],"Brownian":[26,85],"motion":[27],"but,":[28],"any":[30],"realization,":[31],"it":[32,65],"multiplied":[34],"by":[35,53,102],"an":[36,54],"independent":[37],"random":[38],"variable":[39],"properly":[40],"distributed.":[41],"The":[42],"resulting":[43],"probability":[44],"density":[45],"function":[46],"displacement":[49],"can":[50],"be":[51,68],"represented":[52],"integral":[55],"formula":[56],"of":[57,73,89],"subordination":[58],"type":[59],"and,":[60],"single-point":[63],"case,":[64],"emerges":[66],"equal":[69],"solution":[72],"spatially":[75],"symmetric":[76],"space-time":[77],"equation.":[80],"Due":[81],"motion,":[86],"class":[88],"processes":[91],"self-similar":[93],"with":[94],"stationary":[95],"increments":[96],"nature":[98],"and":[99,105,123],"uniquely":[100],"defined":[101],"mean":[104],"auto-covariance":[107],"structure":[108],"analogously":[109],"Gaussian":[112,126],"processes.":[113],"Special":[114],"cases":[115],"are":[116],"time-fractional":[118],"diffusion,":[119],"space-fractional":[121],"classical":[125],"diffusion.":[127]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}