Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d⩾2), which are characterized by a sum of step lengths which is fixed and taken to be 1 without loss of generality, are named “Dirichlet” when this constraint is realized via a...

In this note we highlight the role of fractional linear birth and linear death processes, recently studied in Orsingher et al. (2010) [5] and Orsingher and Polito (2010) [6], in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal...

We investigate the solution of space–time fractional diffusion equations with a generalized Riemann–Liouville time fractional derivative and Riesz–Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation....

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The series for the exact moments, if not the distribution...

Older and recent papers have claimed that a 1/f spectrum can be associated with a sum of pulses arising from a one-dimensional diffusion process. This claim is fallacious since diffusion refers to a collective stochastic process, being the sum of random flights, which constitute the...

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to...

Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M1-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric α-stable Lévy process. The time change is given by the inverse...

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov–Feller equations for the probabilities at...