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A generalization of the space-fractional Poisson process and its connection to some Lévy processes
journal contribution
posted on 2023-06-09, 00:34 authored by Federico Polito, Enrico ScalasThe space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related to a specific subordinator for which it is possible to explicitly write the characterizing Lévy measure. Connections are highlighted to Prabhakar derivatives, specific convolution-type integral operators. Finally, we study the effect of introducing Prabhakar derivatives also in time.
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Publication status
- Published
File Version
- Published version
Journal
Electronic Communications in ProbabilityISSN
1083-589XPublisher
Institute of Mathematical StatisticsExternal DOI
Volume
21Page range
20-34Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2016-03-15First Open Access (FOA) Date
2016-03-15First Compliant Deposit (FCD) Date
2016-03-14Usage metrics
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