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A generalization of the space-fractional Poisson process and its connection to some Levy processes
- Source :
- Electron. Commun. Probab.
- Publication Year :
- 2016
- Publisher :
- UNIV WASHINGTON, DEPT MATHEMATICS, 2016.
-
Abstract
- This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It turns out that this generalization can be put in relation to a specific subordination of a homogeneous Poisson process by means of a subordinator for which it is possible to express the characterizing L\'evy measure explicitly. Moreover, the law of this subordinator solves a one-sided first-order differential equation in which a particular convolution-type integral operator appears, called Prabhakar derivative. In the last section of the paper, a similar model is introduced in which the Prabhakar derivative also acts in time. In this case, too, the probability generating function of the corresponding process and the probability distribution are determined.
- Subjects :
- Statistics and Probability
Generalization
Subordinator
time-change
Prabhakar derivative
subordination
Poisson distribution
Space (mathematics)
01 natural sciences
Lévy process
Measure (mathematics)
010104 statistics & probability
symbols.namesake
QA273
Applied mathematics
60G22
0101 mathematics
Mathematics
010102 general mathematics
Prabhakar integral
fractional point processes
Connection (mathematics)
Lévy processes
symbols
Statistics, Probability and Uncertainty
Fractional Poisson process
Fractional point processes, Lévy processes, Prabhakar integral, Prabhakar derivative, Time-change, Subordination
26A33
60G51
Mathematics - Probability
Subjects
Details
- Language :
- Italian
- ISSN :
- 1083589X
- Database :
- OpenAIRE
- Journal :
- Electron. Commun. Probab.
- Accession number :
- edsair.doi.dedup.....59a298942b9c0e9978628f78eb022a03