Domingo, D orcid.org/0000-0001-8276-6779, d’Onofrio, A and Flandoli, F (2017) Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation. Journal of Mathematical Physics, 58 (3). 033301. ISSN 0022-2488
Abstract
An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show that the aforementioned procedure can be fallacious and lead to incorrect results. We indeed provide a counter-example concerning one of the most employed bounded noises, hereafter called Tsallis-Stariolo-Borland (TSB) noise, which admits the well known Tsallis q-statistics as stationary density. In fact, we show that for negative values of the Tsallis parameter q (corresponding to sufficiently large diffusion coefficient of the stochastic force), the motion resulting from the overdamped approximation is unbounded. We then investigate the cause of the failure of Kramers first type approximation, and we formally show that the solutions of the full Newtonian non-approximated model are bounded, following the physical intuition. Finally, we provide a new family of bounded noises extending the TSB noise, the boundedness of whose solutions we formally show.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Domingo, D , d’Onofrio, A and Flandoli, F (2017) Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation. Journal of Mathematical Physics, 58 (3). 033301. ISSN 0022-2488, and may be found at https://doi.org/10.1063/1.4977081. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Jul 2019 12:02 |
Last Modified: | 10 Jul 2019 12:02 |
Status: | Published |
Publisher: | AIP Publishing |
Identification Number: | 10.1063/1.4977081 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148355 |