On discrete time Prabhakar-generalized fractional Poisson processes and related stochastic dynamics

Recently the so-called Prabhakar generalization of fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal waiting times between events are IID continuous random variables. present paper we analyze discrete-time counterparts: Renewal processes with integer interarrival which converge in well-scaled continuous-time limits Prabhakar-generalized process. These exhibit non-Markovian features and long-time memory effects. We recover special choices parameters versions classical cases, such as Bernoulli standard approximations process, respectively. derive difference equations generalized type that govern these discrete time-processes where known evolution recovered. also develop Montroll–Weiss fashion “Prabhakar Discrete-time walk (DTRW)” a on graph time-changed version Kolmogorov–Feller governing resulting stochastic motion. Prabhakar-discrete-time open promising field capturing several aspects dynamics complex systems.