On the fractional Poisson process and the discretized stable subordinator

Abstract

The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed these two processes, concretely the corresponding counting number and Erlang processes, the latter being the processes inverse to the former. Furthermore we have obtained the diffusion limits of all these processes by well-scaled refinement of waiting times and jumps

30 pages, 4 figures. A preliminary version of this paper was an invited talk given by R. Gorenflo at the Conference ICMS2011, held at the International Centre of Mathematical Sciences, Pala-Kerala (India) 3-5 January 2011, devoted to Prof Mathai on the occasion of his 75 birthday

References in corpus (6)

• Fractional processes: from Poisson to branching one
• Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories
• Full characterization of the fractional Poisson process
• Subordination Pathways to Fractional Diffusion
• Mittag-Leffler Waiting Time, Power Laws,Rarefaction, Continuous Time Random Walk, Diffusion Limit
• Laplace-Laplace analysis of the fractional Poisson process

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• On Densities of the Product, Quotient and Power of Independent Subordinators
• Generalized fractional Poisson process and related stochastic dynamics
• Continuous time random walk and diffusion with generalized fractional Poisson process
• On Discrete Time Prabhakar-Generalized Fractional Poisson Processes and Related Stochastic Dynamics
• Biased continuous-time random walks with Mittag-Leffler jumps
• Generalization of the fractional Poisson distribution
• Squirrels can remember little: A random walk with jump reversals induced by a discrete-time renewal process
• Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes
• A biorthogonal approach to the infinite dimensional fractional Poisson measure
• Prabhakar discrete-time generalization of the time-fractional Poisson process and related random walks