Some probabilistic properties of fractional point processes

Handle URI:
http://hdl.handle.net/10754/625048
Title:
Some probabilistic properties of fractional point processes
Authors:
Garra, Roberto; Orsingher, Enzo; Scavino, Marco ( 0000-0001-5114-853X )
Abstract:
In this article, the first hitting times of generalized Poisson processes N-f (t), related to Bernstein functions f are studied. For the spacefractional Poisson processes, N alpha (t), t > 0 ( corresponding to f = x alpha), the hitting probabilities P{T-k(alpha) < infinity} are explicitly obtained and analyzed. The processes N-f (t) are time-changed Poisson processes N( H-f (t)) with subordinators H-f (t) and here we study N(Sigma H-n(j= 1)f j (t)) and obtain probabilistic features of these extended counting processes. A section of the paper is devoted to processes of the form N( G(H,v) (t)) where G(H,v) (t) are generalized grey Brownian motions. This involves the theory of time-dependent fractional operators of the McBride form. While the time-fractional Poisson process is a renewal process, we prove that the space-time Poisson process is no longer a renewal process.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Garra R, Orsingher E, Scavino M (2017) Some probabilistic properties of fractional point processes. Stochastic Analysis and Applications 35: 701–718. Available: http://dx.doi.org/10.1080/07362994.2017.1308831.
Publisher:
Informa UK Limited
Journal:
Stochastic Analysis and Applications
Issue Date:
16-May-2017
DOI:
10.1080/07362994.2017.1308831
Type:
Article
ISSN:
0736-2994; 1532-9356
Additional Links:
http://www.tandfonline.com/doi/full/10.1080/07362994.2017.1308831
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGarra, Robertoen
dc.contributor.authorOrsingher, Enzoen
dc.contributor.authorScavino, Marcoen
dc.date.accessioned2017-06-19T06:27:28Z-
dc.date.available2017-06-19T06:27:28Z-
dc.date.issued2017-05-16en
dc.identifier.citationGarra R, Orsingher E, Scavino M (2017) Some probabilistic properties of fractional point processes. Stochastic Analysis and Applications 35: 701–718. Available: http://dx.doi.org/10.1080/07362994.2017.1308831.en
dc.identifier.issn0736-2994en
dc.identifier.issn1532-9356en
dc.identifier.doi10.1080/07362994.2017.1308831en
dc.identifier.urihttp://hdl.handle.net/10754/625048-
dc.description.abstractIn this article, the first hitting times of generalized Poisson processes N-f (t), related to Bernstein functions f are studied. For the spacefractional Poisson processes, N alpha (t), t > 0 ( corresponding to f = x alpha), the hitting probabilities P{T-k(alpha) < infinity} are explicitly obtained and analyzed. The processes N-f (t) are time-changed Poisson processes N( H-f (t)) with subordinators H-f (t) and here we study N(Sigma H-n(j= 1)f j (t)) and obtain probabilistic features of these extended counting processes. A section of the paper is devoted to processes of the form N( G(H,v) (t)) where G(H,v) (t) are generalized grey Brownian motions. This involves the theory of time-dependent fractional operators of the McBride form. While the time-fractional Poisson process is a renewal process, we prove that the space-time Poisson process is no longer a renewal process.en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/07362994.2017.1308831en
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Analysis and Applications on 16 May 2017, available online: http://wwww.tandfonline.com/10.1080/07362994.2017.1308831.en
dc.subjectFractional point processesen
dc.subjectBernstein functionsen
dc.subjectspace-time fractional Poisson processesen
dc.subjectgrey Brownian motionen
dc.titleSome probabilistic properties of fractional point processesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalStochastic Analysis and Applicationsen
dc.eprint.versionPost-printen
dc.contributor.institutionDipartimento di Scienze Statistiche, “La Sapienza,” Università di Roma, Roma, Italyen
dc.contributor.institutionInstituto de Estadística (IESTA), Universidad de la Republica, Montevideo, Uruguayen
kaust.authorScavino, Marcoen
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