Some multi-dimensional nonlinear partial differential equations reduce to a linear equation
in fewer dimensions after imposing one additional constraint. A large class of useful …

We define the classic Goldstein-Kac telegraph process performed by a particle that moves
on the real line with some finite constant speed and alternates between two possible …

It was recently shown that, owing to the turbulent nature of the solar wind, the interplanetary
magnetic field lines can be well described by stochastic Parker spirals. These are …

Markov Random Flights is the first systematic presentation of the theory of Markov random
flights in the Euclidean spaces of different dimensions. Markov random flights is a stochastic …

An analytic model for the angular dispersion of magnetic field lines resulting from the
turbulence in the solar wind and at the solar source surface is presented. The heliospheric …

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most
general form with two fractional derivatives of distinct orders. The solutions are given as …

This paper investigates solutions of hyperbolic diffusion equations in R 3 with random initial
conditions. The solutions are given as spatial-temporal random fields. Their restrictions to …

We consider the symmetric Markov random flight, also called the persistent random walk,
performed by a particle that moves at constant finite speed in the Euclidean space R m, m≥ …

The ubiquitous telegrapher's equation is presented in the context of a non-local-in-time
master equation on the lattice. From the exact solution of this transport equation, for different …

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral
methods. Strong, weak, and almost sure convergence rates for the proposed numerical …