7 papers
Most Probable KAM Tori in Stochastic Hamiltonian Systems Driven by Multiplicative Noise
Xinze Zhang, Yong Li, Xue Yang
This paper investigates the effect of state-dependent multiplicative noise on the integrable structure of Hamiltonian systems. Under a local high-dimensional Lamperti-type conditio…
The LLN and CLT for the statistical ensembles of discrete integrable Hamiltonian systems
Xinyu Liu, Xinze Zhang, Yong Li
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addr…
Persistence of Invariant Tori for Stochastic Nonlinear Schrödinger in the Sense of Most Probable Paths
Xinze Zhang, Yong Li, Kaizhi Wang
This paper investigates the application of KAM theory to the stochastic nonlinear Schrödinger equation on infinite lattices, focusing on the stability of low-dimensional invariant…
Most Probable KAM Tori in Stochastic Hamiltonian Systems
Xinze Zhang, Yong Li
This paper investigates in depth how stochastic perturbations affect the integrable structure of Hamiltonian systems and develops a KAM theory for stochastic Hamiltonian dynamics,…
Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise
Xinze Zhang, Yong Li
This paper investigates the Onsager-Machlup functional of stochastic lattice dynamical systems (SLDSs) driven by time-varying noise. We extend the Onsager-Machlup functional from f…
Poisson stability of solutions for stochastic evolution equations driven by fractional Brownian motion
Xinze Zhang, Li Yong, Xue Yang
In this paper, we study the problem of Poisson stability of solutions for stochastic semi-linear evolution equation driven by fractional Brownian motion \mathrm{d} X(t)= \left( AX(…
Onsager-Machlup functional for stochastic differential equations with time-varying noise
Xinze Zhang, Yong Li
This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations with time-varying noise of the α-Hölder, 0<α<1/4, dXt =f(t,Xt)dt+g(t)dWt. Our…