Linear response theory for nonlinear stochastic differential equations with α-stable Levy noises

发布时间：2022-09-27 作者：77779193永利官网浏览次数：

Speaker:	张琦	DateTime:	2022年9月30日下午14: 30--15: 30
Brief Introduction to Speaker: 张琦博士，北京雁栖湖应用数学研究院		Place:	腾讯会议：388-280-583 会议密码：220930
Abstract:We establish a linear response theory for stochastic differential equations driven by an α-stable Lévy noise (1< α<2). We first prove existence and uniqueness of the invariant measure by the Bogoliubov-Krylov argument. Then we obtain some regularity results for the probability density of its invariant measure by establishing the a priori estimate of the corresponding stationary Fokker-Planck equation. Finally, by the perturbation property of the Markov semigroup, we derive the linear response theory. This result is a general fluctuation-dissipation relation between the response of the system to the external perturbations and the Lévy type fluctuations at a steady state.