Existence of periodic solutions in distribution for stochastic Newtonian systems

DOI10.1007/s10955-020-02583-3zbMath1452.34063OpenAlexW3037451953MaRDI QIDQ2202306

Xue Yang, Xiaomeng Jiang, Yong Li

Publication date: 18 September 2020

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-020-02583-3

zbMATH Keywords

Lyapunov's methodWong-Zakai approximationsLevinson's conjecturestochastic Newtonian systemsperiodic solutions in distribution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Random vibrations in mechanics of particles and systems (70L05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary differential equations and systems with randomness (34F05) Applications of operator theory to differential and integral equations (47N20) Nonautonomous smooth dynamical systems (37C60) Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) (34A06)

Related Items (8)

LaSalle-type stationary oscillation principle for stochastic affine periodic systems ⋮ Periodic solutions of stochastic functional differential equations with jumps via viability ⋮ Poisson stable solutions for stochastic functional evolution equations with infinite delay ⋮ Poisson stable solutions and solution maps for stochastic functional differential equations ⋮ Random periodic solutions of SDEs: existence, uniqueness and numerical issues ⋮ Unnamed Item ⋮ Periodic solutions in distribution of stochastic lattice differential equations ⋮ Periodic solutions in distribution of mean-field stochastic differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Favard separation method for almost periodic stochastic differential equations
• Smooth approximation of stochastic differential equations
• Anticipating random periodic solutions. I: SDEs with multiplicative linear noise.
• Periodic solutions of Fokker-Planck equations
• Square-mean pseudo almost automorphic process and its application to stochastic evolution equations
• Unified boundedness, periodicity, and stability in ordinary and functional differential equations
• Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
• A Wong-Zakai theorem for stochastic PDEs
• Random periodic solutions of random dynamical systems
• Stability and periodic solutions of ordinary and functional differential equations
• Uniform ultimate boundedness and periodicity in functional differential equations
• Stability theory and the existence of periodic solutions and almost periodic solutions
• A class of approximations of Brownian motion
• On the gap between deterministic and stochastic ordinary differential equations
• Asymptotic stability and smooth Lyapunov functions
• Time-periodic solutions of the time-dependent Ginzburg-Landau equation of superconductivity
• Periodic solutions for dissipative-repulsive systems
• Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems
• The Wong-Zakai approximations of invariant manifolds and foliations for stochastic evolution equations
• On the Kohn-Sham equations with periodic background potentials
• Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations
• Wong-Zakai approximations and center manifolds of stochastic differential equations
• Existence of periodic probability solutions to Fokker-Planck equations with applications
• On the relation between ordinary and stochastic differential equations
• Uniform persistence and periodic solution of chemostat-type model with antibiotic
• Transformation theory of non-linear differential equations of the second order
• An interpretation of stochastic differential equations as ordinary differential equations which depend on the sample point
• An approximation theorem of wong-zakai type for nonlinear stochastic partial differential equations
• On the Convergence of Ordinary Integrals to Stochastic Integrals
• Some Fixed Point Theorems for Compact Maps and Flows in Banach Spaces
• Time operators and time crystals: self-adjointness by topology change
• Probability Theory

This page was built for publication: Existence of periodic solutions in distribution for stochastic Newtonian systems