Properties of bounded stochastic processes employed in biophysics

Domingo, Dario; d’Onofrio, Alberto; Flandoli, Franco

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.

Citation

Domingo, D., d’Onofrio, A., & Flandoli, F. (2020). Properties of bounded stochastic processes employed in biophysics. Stochastic Analysis and Applications, 38(2), 277-306. https://doi.org/10.1080/07362994.2019.1694416

• Journal Article Type: Article
• Acceptance Date: Nov 13, 2019
• Online Publication Date: Dec 3, 2019
• Publication Date: 2020
• Deposit Date: Dec 12, 2019
• Publicly Available Date: Dec 3, 2020
• Journal: Stochastic Analysis and Applications
• Print ISSN: 0736-2994
• Electronic ISSN: 1532-9356
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 2
• Pages: 277-306
• DOI: https://doi.org/10.1080/07362994.2019.1694416
• Public URL: https://durham-repository.worktribe.com/output/1311882