论文标题
随机动力学系统不变测量的零噪声限制的浓度
The concentration of zero-noise limits of invariant measures for stochastic dynamical systems
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^d $与局部Lipschitz连续系数和多个ergodic状态下定义的随机微分方程的零噪声限制的浓度现象。在某些耗散条件下，通过使用lyapunov样函数和大偏差方法，我们估计稳定集合，不稳定集合的社区及其补体的社区中的不变措施。我们的结果表明，不变的度量集中在稳定集的交点上，其中成本功能$ W（k_i）$被最小化，而相应的确定性系统的Birkhoff中心由于噪声趋向于零。此外，我们证明了不变措施的巨大偏差原则。在本文的最后，我们提供了一些明确的示例及其数值模拟。
In this paper, we study concentration phenomena of zero-noise limits of invariant measures for stochastic differential equations defined on $\mathbb{R}^d$ with locally Lipschitz continuous coefficients and more than one ergodic state. Under some dissipative conditions, by using Lyapunov-like functions and large deviations methods, we estimate the invariant measures in neighborhoods of stable sets, neighborhoods of unstable sets and their complement, respectively. Our result illustrates that invariant measures concentrate on the intersection of stable sets where a cost functional $W(K_i)$ is minimized and the Birkhoff center of the corresponding deterministic systems as noise tends down to zero. Furthermore, we prove the large deviations principle of invariant measures. At the end of this paper, we provide some explicit examples and their numerical simulations.
