{"id":"https://openalex.org/W1916869002","doi":null,"title":"On a fractional jump process with two kinds of jumps and its connection with the Poisson process","display_name":"On a fractional jump process with two kinds of jumps and its connection with the Poisson process","publication_year":2015,"publication_date":"2015-03-22","ids":{"openalex":"https://openalex.org/W1916869002","mag":"1916869002"},"language":"en","primary_location":{"id":"mag:1916869002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.06486","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1503.06486","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053483603","display_name":"Antonio Di Crescenzo","orcid":"https://orcid.org/0000-0003-4751-7341","observed_orcids":["https://orcid.org/0000-0003-4751-7341"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antonio Di Crescenzo","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4751-7341","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001259031","display_name":"Barbara Martinucci","orcid":"https://orcid.org/0000-0001-8340-4200","observed_orcids":["https://orcid.org/0000-0001-8340-4200"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barbara Martinucci","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8340-4200","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040947802","display_name":"Alessandra Meoli","orcid":"https://orcid.org/0000-0002-3516-9530","observed_orcids":["https://orcid.org/0000-0002-3516-9530"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alessandra Meoli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9731000065803528,"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":0.9731000065803528,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.003800000064074993,"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"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-poisson-process","display_name":"fractional Poisson process","score":0.7239999771118164},{"id":"https://openalex.org/keywords/generalized-mittag-leffler-function","display_name":"generalized Mittag-Leffler function","score":0.8730000257492065},{"id":"https://openalex.org/keywords/subordinating-conjunctions","display_name":"subordinating conjunctions","score":0.8820000290870667},{"id":"https://openalex.org/keywords/fractional-cauchy-problem","display_name":"fractional Cauchy problem","score":0.9539999961853027},{"id":"https://openalex.org/keywords/first-passage-time","display_name":"first passage time","score":0.8230000138282776},{"id":"https://openalex.org/keywords/waiting-time-distribution","display_name":"waiting time distribution","score":0.8529999852180481},{"id":"https://openalex.org/keywords/convergence-in-probability","display_name":"convergence in probability","score":0.628000020980835},{"id":"https://openalex.org/keywords/differential-difference-equations","display_name":"differential-difference equations","score":0.6499999761581421}],"concepts":[{"id":"https://openalex.org/C2781362121","wikidata":"https://www.wikidata.org/wiki/Q7631785","display_name":"Subordinator","level":3,"score":0.8549750447273254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6881306171417236},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6527359485626221},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6526179313659668},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6095178127288818},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5640787482261658},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5297744274139404},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.4845539629459381},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.46883314847946167},{"id":"https://openalex.org/C133338972","wikidata":"https://www.wikidata.org/wiki/Q2055750","display_name":"Compound Poisson process","level":4,"score":0.4538898766040802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36652109026908875},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.29025283455848694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2439582347869873},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19169241189956665},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13330066204071045},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10291042923927307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07717251777648926}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:1916869002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.06486","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:1916869002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.06486","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W69681244","https://openalex.org/W1999062253","https://openalex.org/W2000952269","https://openalex.org/W2006322905","https://openalex.org/W2027112235","https://openalex.org/W2043406699","https://openalex.org/W2072534786","https://openalex.org/W2125528389","https://openalex.org/W2132017387","https://openalex.org/W2165139650","https://openalex.org/W3102949077","https://openalex.org/W3118147875"],"related_works":["https://openalex.org/W2300735380","https://openalex.org/W2096217566","https://openalex.org/W4289135218","https://openalex.org/W2795180627","https://openalex.org/W2132017387","https://openalex.org/W2273516843","https://openalex.org/W4385261394","https://openalex.org/W7160422126","https://openalex.org/W1949826380","https://openalex.org/W2521645547"],"abstract_inverted_index":{"We":[0,34,49,115],"consider":[1],"a":[2,16,59,63,70,80,101,108],"fractional":[3,17,65,72,103,127,142],"jump":[4,81,128,157],"process":[5,42,129,158],"with":[6],"jumps":[7],"of":[8,19,39,45,58,69,79,82,96,100,120,125,139,155],"size":[9],"1":[10],"and":[11,68],"2,":[12],"whose":[13],"probabilities":[14],"satisfy":[15],"extension":[18],"the":[20,36,40,89,93,97,112,118,121,126,136,140,149,153,156],"difference-differential":[21],"equations":[22],"$$":[23,33],"\\dfrac{\\mathrm{d}p_{k}(t)":[24],"}{\\mathrm{d}t":[25],"}":[26],"=\\lambda_{2}p_{k-2}(t)+\\lambda_{1}p_{k-1}(t)-(\\lambda_{1}+\\lambda_{2})p_{k}(t),":[27],"\\quad":[28],"k\\geq":[29],"0,":[30],"\\;\\;":[31],"t>0.":[32],"obtain":[35],"probability":[37,164],"law":[38],"resulting":[41],"in":[43,56,130,163],"terms":[44,57],"generalized":[46],"Mittag-Leffler":[47],"functions.":[48],"also":[50,116],"discuss":[51],"two":[52],"equivalent":[53],"representations":[54],"both":[55],"subordinator":[60],"governed":[61],"by":[62,152],"suitable":[64],"Cauchy":[66],"problem,":[67],"compound":[71],"Poisson":[73,104,113,143],"process.":[74,114,144],"The":[75],"first":[76,98,122],"occurrence":[77],"time":[78,95,124],"fixed":[83],"amplitude":[84],"is":[85],"proved":[86],"to":[87,165],"have":[88],"same":[90],"distribution":[91,119,138],"as":[92],"waiting":[94],"event":[99],"classical":[102,141],"process,":[105],"this":[106],"extending":[107],"well-known":[109],"result":[110],"for":[111],"express":[117],"passage":[123],"an":[131],"integral":[132],"form":[133],"that":[134,148],"involves":[135],"joint":[137],"Finally,":[145],"we":[146],"show":[147],"ratios":[150],"given":[151],"powers":[154],"over":[159],"their":[160],"means":[161],"converge":[162],"1.":[166]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
