We develop a comprehensive framework for analyzing full-record statistics, covering record
counts M (t 1), M (t 2),..., their corresponding attainment times TM (t 1), TM (t 2),..., and the …

We investigate the effects of the resetting mechanism to the origin for a random motion on
the real line characterized by two alternating velocities v 1 and v 2. We assume that the …

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 …

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 …

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 …

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 …

This thesis is devoted to the study of extreme value statistics in stochastic processes and
their applications. In the first part, we obtain exact analytical results on the extreme value …

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 …

In this manuscript, we provide a non-asymptotic process level control between the telegraph
process and the Brownian motion with suitable diffusivity constant via a Wasserstein …

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 …