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A Damped Telegraph Random Process with Logistic Stationary Distribution

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Antonio Di Crescenzo  and
Barbara Martinucci
Antonio Di Crescenzo*
Affiliation:
Università degli Studi di Salerno
Barbara Martinucci*
Affiliation:
Università degli Studi di Salerno
*
∗Postal address: Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.
∗Postal address: Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.
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Abstract

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We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given.

Keywords

Alternating random processlogistic stationary distributiondistribution of the maximumfirst passage time

MSC classification

Secondary: 60K15: Markov renewal processes, semi-Markov processes 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 84 - 96
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

This work has been partially supported by Regione Campania and MIUR (PRIN 2008).

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