TY - JOUR

T1 - Some probabilistic properties of fractional point processes

AU - Garra, Roberto

AU - Orsingher, Enzo

AU - Scavino, Marco

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2017/5/16

Y1 - 2017/5/16

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/625048

UR - http://www.tandfonline.com/doi/full/10.1080/07362994.2017.1308831

UR - http://www.scopus.com/inward/record.url?scp=85019502160&partnerID=8YFLogxK

U2 - 10.1080/07362994.2017.1308831

DO - 10.1080/07362994.2017.1308831

M3 - Article

SN - 0736-2994

VL - 35

SP - 701

EP - 718

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 4

ER -