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 …

We study planar random motions with finite velocities, of norm c> 0, along orthogonal
directions and changing at the instants of occurrence of a nonhomogeneous Poisson …

In this paper we present the distribution of the maximum of the asymmetric telegraph
process in an arbitrary time interval [0, t] under the conditions that the initial velocity V (0) is …

We consider the telegraph process with two velocities, a 1> a 2∈ R, and two rates of
reversal, λ 1, λ 2> 0. We study some of its features with respect to the conditional probability …

In a recent work we introduced a semi-Markovian discrete-time generalization of the
telegraph process. We referred to this random walk as the 'squirrel random walk'(SRW). The …

In this note, we present some ideas for describing the distributions of the running
maximum/minimum, first passage times and telegraphic meanders. Explicit formulae for joint …

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 …

In this paper we study the joint distributions of the telegraph process and its maximum
conditioned on the number of changes of direction and the initial velocity. We prove that in …

This chapter is devoted to the various functionals of telegraph processes. First, we present
well-known results on distributions of the telegraph processes distorted by reflecting and …

Abstract The symmetric Goldstein-Kac telegraph process describes the motion of a particle
on the real line moving at some finite constant speed and alternating between the two …