Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

Pearson diffusions are governed by diffusion equations with polynomial coefficients.
Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion …

Stochastic resetting with home returns is widely found in various manifestations in life and
nature. Using the solution to the home return problem in terms of the solution to the …

We introduce a non-homogeneous fractional Poisson process by replacing the time variable
in the fractional Poisson process of renewal type with an appropriate function of time. We …

The recent literature on high frequency financial data includes models that use the
difference of two Poisson processes, and incorporate a Skellam distribution for forward …

We discuss the short-range dependence (SRD) property of the increments of the fractional
Poisson process, called the fractional Poissonian noise. We also establish that the fractional …

We present new properties for the Fractional Poisson process (FPP) and the Fractional
Poisson field on the plane. A martingale characterization for FPPs is given. We extend this …

There is by now an extensive and well-developed theory of weak convergence for moving
averages and continuous-time random walks (CTRWs) with respect to Skorokhod's M1 and …

We have discovered here a duality relation between infinitely divisible subordinators which
can produce both retarding and accelerating anomalous diffusion in the framework of the …

In this article, convolution-type fractional derivatives generated by Dickman subordinator
and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse …