Event Details
Title: Finite-velocity random motions and reset at the origin: Recent advances on transient and limit behaviors.
Speaker: Antonio di Crescenzo (Department of Mathematics, University of Salerno).
Schedule: 9:30-11:00h & 11:30-13:00h.
Abstract:
Stochastic processes for the description of finite-velocity random motions have been largely studied during the last decades. Usually, they refer to the motion of a particle moving with finite speed on the real line, or on more general domains, with alternations between various possible velocities or directions at random times. The basic model is concerning the so-called (integrated) telegraph process, in which the changes of directions of the two possible velocities are governed by the Poisson process.
In this seminar we aim to present some recent results in this research area, involving
- (i) one-dimensional and two-dimensional finite-velocity random motions, such that the random intertimes between consecutive changes of directions are governed by geometric counting processes,
- (ii) inclusion of the resetting mechanism to the origin for the one-dimensional process considered in (i),
- (iii) one-dimensional finite-velocity random motions with instantaneous reset to the origin regulated by Bernoulli trials.
We focus on various features of the considered stochastic processes, including the analysis of the probability laws, the behavior under limit conditions, the mean-square distance between processes, connections with the classical telegraph process.
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