Showing papers by "Barbara Martinucci published in 2018"

Telegraph Process with Elastic Boundary at the Origin

Abstract: We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability α, or reflected upwards, with probability 1−α. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.

A New Model of Campi Flegrei Inflation and Deflation Episodes Based on Brownian Motion Driven by the Telegraph Process

Abstract: A stochastic model to describe the vertical motions in the Campi Flegrei volcanic region is proposed herein, consisting of a Brownian motion process driven by a generalized telegraph process Knowledge on the probability law of this process enables quantitative investigation of some basic parameters regulating the inflation/deflation processes, such as velocities and time constants Statistical analysis was carried out based on linear regression with constraints Predictions of ground displacements and their changing tendency at future time instants were also made Finally, a statistical test on the Brownian component of the process confirmed the goodness of the model

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

Abstract: We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).