6 papers
Large Deviations for the Nonlinear Schrödinger Equation with Randomized Quasi-Periodic Initial Data in Higher Dimensions: Subcritical Case
Fei Xu, Yong Li
We study the cubic weakly nonlinear Schrödinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier…
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…
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 Fractional Stochastic Newton Dynamics with Time-Dependent Noise Intensities
Yanbin Zhu, Xiaomeng Jiang, Yong Li
In this paper, we derive the Onsager--Machlup functional for a second-order Newton-type stochastic system driven by time-dependent fractional noise, \[ X_t'' = f_t(X_t, X_t') + Ï_…
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.…
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(…