Existence of Periodic Solutions in Distribution for Stochastic Newtonian Systems

• Published in: Journal of statistical physics Vol. 181; no. 2; pp. 329 - 363
• Main Authors: Jiang, Xiaomeng, Li, Yong, Yang, Xue
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2020; Springer; Springer Nature B.V
• Subjects: Approximation; Differential equations; Fixed points (mathematics); Mathematical and Computational Physics; Newton's laws of motion; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Levinson’s conjecture; Periodic solutions in distribution; Wong–Zakai approximations; Lyapunov’s method; Stochastic Newtonian systems

Periodic phenomena such as oscillation have been studied for many years. In this paper, we verify the stochastic version of Levinson’s conjecture, which confirmed the existence of stochastic periodic solutions for second order Newtonian systems with dissipativeness. First, we provide a stochastic Du...