Periodic solutions of Fokker-Planck equations

被引：31
|
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
收藏
页码：285 / 298
页数：14
相关论文
共 50 条
  • [1] CONVERGENCE TO PERIODIC PROBABILITY SOLUTIONS IN FOKKER-PLANCK EQUATIONS
    Ji, Min
    Qi, Weiwei
    Shen, Zhongwei
    Yi, Yingfei
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (02) : 1958 - 1992
  • [2] Existence of periodic probability solutions to Fokker-Planck equations with applications
    Ji, Min
    Qi, Weiwei
    Shen, Zhongwei
    Yi, Yingfei
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 277 (11)
  • [3] Existence, Stability and Regularity of Periodic Solutions for Nonlinear Fokker-Planck Equations
    Lucon, Eric
    Poquet, Christophe
    [J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2024, 36 (01) : 633 - 671
  • [4] Lp-solutions of Fokker-Planck equations
    Wei, Jinlong
    Liu, Bin
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 85 : 110 - 124
  • [5] Operator solutions for fractional Fokker-Planck equations
    Gorska, K.
    Penson, K. A.
    Babusci, D.
    Dattoli, G.
    Duchamp, G. H. E.
    [J]. PHYSICAL REVIEW E, 2012, 85 (03):
  • [6] ON THE GAUSSIAN APPROXIMATION FOR SOLUTIONS OF FOKKER-PLANCK EQUATIONS
    KHARRASOV, MK
    ABDULLIN, AU
    [J]. DOKLADY AKADEMII NAUK, 1994, 335 (01) : 32 - 34
  • [7] Generalized solutions to nonlinear Fokker-Planck equations
    Barbu, Viorel
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (04) : 2446 - 2471
  • [8] STEADY-STATE SOLUTIONS OF THE FOKKER-PLANCK EQUATIONS
    ZHENG, Q
    HAO, BL
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 1987, 8 (02) : 153 - 166
  • [9] SINGULARITY OF THE SOLUTIONS OF SOME GENERALIZED FOKKER-PLANCK EQUATIONS
    KREE, P
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1985, 300 (10): : 291 - 294
  • [10] Exact solutions of the Fokker-Planck equations with moving boundaries
    Lo, CF
    [J]. ANNALS OF PHYSICS, 2005, 319 (02) : 326 - 332
12345