We prove large deviation principles for two versions of fractional Poisson processes: the main version is a renewal process, the alternative version is a weighted Poisson process. We also present asymptotic results for the ruin probabilities of an insurance model with a fractional Poisson claim...

A general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations. Non-Poisson...

In terms of the two-parameter Mittag-Leffler function with specified parameters, this paper introduces the Mittag-Leffler vector random field through its finite-dimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two...

We introduce a new distribution useful for positively skewed dataset with heavy tails and refer to it as the “Wright distribution”. Properties involving moments, skewness and kurtosis are studied. Simulation study and derivation of the density function using fractional calculus method are...

In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian and described by the Continuous Time Random Walk model....

Efforts on the fundamentals of the nonextensive thermostatistical formulations of the realistic description of the physical systems have always been underway. In this context, the quantum systems of bosons and fermions are taken into consideration as g-ons. A new formalism of the unified...

In the literature, the deviations from standard behaviors of the solutions of the kinetic equation and the analogous diffusion equation are put forward by investigations which are carried out in the frame of fractional mathematics and nonextensive physics. On the other hand, the physical origins...