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Properties of bounded stochastic processes employed in biophysics.

Domingo, Dario and d’Onofrio, Alberto and Flandoli, Franco (2020) 'Properties of bounded stochastic processes employed in biophysics.', Stochastic analysis and applications., 38 (2). pp. 277-306.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1080/07362994.2019.1694416
Publisher statement:This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic analysis and applications on 3 December 2019, available online: http://www.tandfonline.com/10.1080/07362994.2019.1694416
Date accepted:13 November 2019
Date deposited:12 December 2019
Date of first online publication:03 December 2019
Date first made open access:03 December 2020

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