We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion
in an orientation that stochastically rotates by 90∘ at a constant rate, clockwise or …

We study a stochastic process which describes the dynamics of a particle performing a finite-
velocity random motion whose velocities alternate cyclically. We consider two cases, in …

This paper is devoted to the detailed analysis of three-dimensional motions in R 3 with
orthogonal directions switching at Poisson times and moving with constant speed c> 0. The …

In this paper we give an explicit solution to Dzherbashyan-Caputo-fractional Cauchy
problems related to equations with derivatives of order νk, for k non-negative integer and ν> …

Confined active particles constitute simple, yet realistic, examples of systems that converge
into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial …

Run-and-tumble is a basic model of persistent motion and a motility strategy widespread in
micro-organisms and individual cells. In many natural settings, movement occurs in the …

We present a detailed analysis of random motions moving in higher spaces with a natural
number of velocities. In the case of the so-called minimal random dynamics, under some …

We consider the random motion of a particle that moves with constant velocity in R 3. The
particle can move along four different directions that are attained cyclically. It follows that the …

We present a reflection principle for a wide class of symmetric random motions with finite
velocities. We propose a deterministic argument which is then applied to trajectories of …

We study a planar random motion $\big (X (t),\, Y (t)\big) $ with orthogonal directions, where
the direction switches are governed by a homogeneous Poisson process. At each Poisson …