Exponential almost sure synchronization of one-dimensional diffusions with nonregular coefficients. Issue 4 (4th July 2021)

• Record Type: Journal Article
• Authors: Aryasova, Olga; Pilipenko, Andrey; Roelly, Sylvie
• Is Part Of: Stochastic analysis and applications. Volume 39:Issue 4(2021)
• Page Start: 631
• Page End: 642
• Publication Date: 2021-07-04
• Subjects: Stochastic differential equation (SDE) -- singular drift -- synchronization; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1823234
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We study the asymptotic behavior of a real-valued diffusion whose nonregular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge almost sure to one another at an exponential explicit rate as soon as the dissipative coefficient is large enough. A similar result in Lp is obtained.