具有乘性噪声和非线性阻尼的随机离散波动方程不变测度的大偏差原理

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-05-28 DOI:10.1016/j.bulsci.2025.103670

Yongkang Zhang, Xiaojun Li

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引用次数: 0

摘要

本文研究了定义在n维整数集上的一类具有乘性噪声和非线性阻尼的离散波动方程的不变测度的大偏差原理。我们首先建立了随机系统不变测度的存在性，并分析了这些测度在噪声强度趋近于零时的极限行为。其次，我们证明了随机系统解的Freidlin-Wentzell一致大偏差和Dembo-Zeitouni一致大偏差。最后，我们结合指数概率估计和基于加权空间的参数推导出不变测度的大偏差。

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Large deviation principles of invariant measures of stochastic discrete wave equations with multiplicative noise and nonlinear damping

In this paper, we study the large deviation principle of invariant measures of a class of discrete wave equations with multiplicative noise and nonlinear damping, defined on a N-dimensional integer set. We first establish the existence of invariant measures for the stochastic system and analyze the limiting behavior of these measures as the noise intensity approaches zero. Next, we prove the Freidlin-Wentzell uniform large deviations and the Dembo-Zeitouni uniform large deviations of the solutions of the stochastic system. Lastly, we derive the large deviations of invariant measures by combining exponential probability estimates and arguments based on weighted spaces.

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