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math.DS2026
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…
math.PR2026
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…
math.DS2026
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') + σ_t…