论文标题
具有$α$稳定的lévy噪声的非线性随机微分方程的线性响应理论
Linear Response Theory for Nonlinear Stochastic Differential Equations with $α$-stable Lévy Noises
论文作者
论文摘要
我们考虑由$α$稳定的lévy工艺驱动的非线性随机微分方程（$ 1 <α<2 $）。我们首先通过建立相应固定fokker-Planck方程的先验估计值来获得其不变度度量的概率密度的一些规律性结果。然后，通过对Markov Semigroup的kolmogorov向后方程和扰动特性的先验估计，我们得出了响应函数，并将非平衡统计力学中著名的线性响应理论推广到非高斯随机动力学系统。
We consider a nonlinear stochastic differential equation driven by an $α$-stable Lévy process ($1<α<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a priori estimate of the corresponding stationary Fokker-Planck equation. Then by the a priori estimate of Kolmogorov backward equations and the perturbation property of Markov semigroup, we derive the response function and generalize the famous linear response theory in nonequilibrium statistical mechanics to non-Gaussian stochastic dynamic systems.
