Domingo, D orcid.org/0000-0001-8276-6779, d’Onofrio, A and Flandoli, F (2020) Properties of bounded stochastic processes employed in biophysics. Stochastic Analysis and Applications, 38 (2). pp. 277-306. ISSN 0736-2994
Abstract
Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Taylor & Francis Group, LLC. This is an author produced version of an article published in Stochastic Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Bounded noises; stochastic differential equations; strong uniqueness; local times; transformations |
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: | 02 Jan 2020 11:42 |
Last Modified: | 03 Dec 2020 01:40 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/07362994.2019.1694416 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154939 |