Periodic solutions of Fokker-Planck equations

被引：36

作者：

Chen, Feng ^{[1
,2
]}

Han, Yuecai ^{[3
]}

Li, Yong ^{[1
,2
,3
,4
]}

Yang, Xue ^{[1
,2
,3
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Changchun 130024, Peoples R China

[3] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

[4] Jilin Univ, State Key Lab Automot Simulat & Control, Changchun 130025, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 01期

关键词：

Fokker-Planck equations; Stochastic differential equations; Periodic solutions; Halanay's criterion; Lyapunov's functions; STOCHASTIC DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.jde.2017.02.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：285 / 298

页数：14

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