Periodic solutions of Fokker-Planck equations
Periodic solutions of Fokker-Planck equations
复制标题
福克-普朗克方程的周期解
DOI：
10.1016/j.jde.2017.02.032
复制
发表时间：
2017
影响因子：
2.4
通讯作者：
Yang Xue
中科院分区：
文献类型：
--
作者：
Chen Feng;Han Yuecai;Li Yong;Yang Xue
本文通过讨论一类随机微分方程周期解的存在性，得到了Fokker-Planck方程周期解的存在性.为了证明随机微分方程周期解的存在性，给出了一个类似于Halanay准则的新准则。实际上，该准则类似于大数定律。在此基础上，利用李雅普诺夫方法建立了随机（泛函）微分方程周期解的分布存在性。
In this paper, the existence of periodic solutions of Fokker–Planck equations is obtained by discussing the existence of periodic solutions in distribution for some stochastic differential equations. To prove the existence of periodic solutions in distribution for stochastic differential equations, a new criterion analogous to Halanay's criterion is given. Actually, the criterion is similar to a law of large numbers. Based on this criterion, the existence of periodic solutions in distribution for stochastic (functional) differential equations is established by Lyapunov's method.