论文标题
二次响应和零噪声限制中不变度量的收敛速度
Quadratic response and speed of convergence of invariant measures in the zero-noise limit
论文作者
论文摘要
我们从定量的角度研究了零噪声极限的随机稳定性。 我们认为圆圈的平滑扩展地图受到添加噪声的扰动。我们表明，在这种情况下，零噪声极限具有二次收敛速度，如Lin在数值实验之后，林（Lin）在2005年的猜想（请参阅Arxiv：Math/0406201）。这是通过在泰勒对固定度量对小噪声扰动的响应扩展中的第一和第二项的明确公式来获得的。这些术语取决于动态的重要特征和噪声的噪声，这是其平均值和差异。 我们还从定量的角度考虑了零噪声限制，用于分段扩展地图，显示了这种情况下收敛速度的估计值。
We study the stochastic stability in the zero-noise limit from a quantitative point of view. We consider smooth expanding maps of the circle, perturbed by additive noise. We show that in this case the zero-noise limit has a quadratic speed of convergence, as conjectured by Lin, in 2005, after numerical experiments (see arXiv:math/0406201 ). This is obtained by providing an explicit formula for the first and second term in the Taylor's expansion of the response of the stationary measure to the small noise perturbation. These terms depend on important features of the dynamics and of the noise which is perturbing it, as its average and variance. We also consider the zero-noise limit from a quantitative point of view for piecewise expanding maps showing estimates for the speed of convergence in this case.
