A generalization of the space-fractional Poisson process and its connection to some Levy processes

作者：Polito Federico^*; Scalas Enrico

来源：Electronic Communications in Probability, 2016, 21(0).

DOI：10.1214/16-ECP4383

• fractional point processes
• Levy processes
• Prabhakar integral
• Prabhakar derivative
• time-change
• subordination

The 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 Levy 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 Levy measure. Connections are highlighted to Prabhakar derivatives, specific convolution-type integral operators. Finally, we study the effect of introducing Prabhakar derivatives also in time.

• 出版日期2016