Crimaldi, Irene and Di Crescenzo, Antonio and Iuliano, Antonella and Martinucci, Barbara A generalized telegraph process with velocity driven by random trials. Advances in applied probability, 45 (4). pp. 1111-1136. ISSN 0001-8678 (2013)
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Abstract
We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pòlya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of Pòlya trials and intertimes having first Gamma and then exponential distributions with constant rates.
| Item Type: | Article |
|---|---|
| Identification Number: | https://doi.org/10.1239/aap/1386857860 |
| Uncontrolled Keywords: | telegraph process, random intertimes, random velocities, Bernoulli scheme, Pòlya urn model |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Research Area: | Economics and Institutional Change |
| Depositing User: | Irene Crimaldi |
| Date Deposited: | 23 Dec 2013 08:31 |
| Last Modified: | 23 Dec 2013 08:31 |
| URI: | http://eprints.imtlucca.it/id/eprint/2084 |
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