The aim of this paper is to analyze a class of random processes which models the motion of a particle on the real line with random velocity and subject to the action of friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and moment generating functions of the position reached by the particle at time t > 0. We are able to derive the explicit probability distributions in a few cases. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we consider randomly varying time. Essentially, we consider two different types of random time, namely Bessel and gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, exponential). For the random processes built by means of these compositions, we derive the probability distributions for a fixed number of Poisson events. Some remarks on possible extensions to random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion.

STOCHASTIC VELOCITY MOTIONS AND PROCESSES WITH RANDOM TIME / DE GREGORIO, Alessandro. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - 42:4(2010), pp. 1028-1056. [10.1239/aap/1293113150]

STOCHASTIC VELOCITY MOTIONS AND PROCESSES WITH RANDOM TIME

DE GREGORIO, ALESSANDRO
2010

Abstract

The aim of this paper is to analyze a class of random processes which models the motion of a particle on the real line with random velocity and subject to the action of friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and moment generating functions of the position reached by the particle at time t > 0. We are able to derive the explicit probability distributions in a few cases. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we consider randomly varying time. Essentially, we consider two different types of random time, namely Bessel and gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, exponential). For the random processes built by means of these compositions, we derive the probability distributions for a fixed number of Poisson events. Some remarks on possible extensions to random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion.
2010
bessel process; gamma process; iterated brownian motion; laplace distribution; random flight; random time; struve function; telegraph process
01 Pubblicazione su rivista::01a Articolo in rivista
STOCHASTIC VELOCITY MOTIONS AND PROCESSES WITH RANDOM TIME / DE GREGORIO, Alessandro. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - 42:4(2010), pp. 1028-1056. [10.1239/aap/1293113150]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/377024
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