Almost sure and moment exponential stability of Euler-Maruyama method for non-autonomous stochastic differential equations

被引：0
|
作者：
Mo Haoyi [1 ,2 ]
Deng Feiqi [1 ]
Ren Hongwei [1 ]
机构：
[1] South China Univ Technol, Syst Engn Inst, Guangzhou 510006, Guangdong, Peoples R China
[2] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510006, Guangdong, Peoples R China
来源：
2015 34TH CHINESE CONTROL CONFERENCE (CCC) | 2015年
关键词：
Non-autonomous stochastic differential equation; Euler-Maruyama method; Almost sure exponential stability; Moment exponential stability; Linear growth condition; MEAN-SQUARE STABILITY; THETA-METHOD;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
For autonomous stochastic differential equations (SDEs), it has been shown that the Euler-Maruyama (EM) method produces almost sure exponential stability and moment exponential stability of SDEs under some conditions which include the linear growth condition. In this work, we extend these results to non-autonomous SDEs, and prove that the exact solution is almost sure exponential stability and moment exponential stability under the local linear growth condition which is weaker than the linear growth condition. It is shown that the EM method maintains corresponding stability. A numerical example is presented to illustrate the effectiveness of this result.
引用
收藏
页码：1655 / 1659
页数：5
相关论文
共 50 条
  • [41] Mean-square stability of the Euler-Maruyama method for stochastic differential delay equations with jumps
    Tan, Jianguo
    Wang, Hongli
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (02) : 421 - 429
  • [42] Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments
    Geng, Yidan
    Song, Minghui
    Lu, Yulan
    Liu, Mingzhu
    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2021, 14 (01): : 194 - 218
  • [43] STABILITY ANALYSIS BETWEEN THE HYBRID STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH JUMPS AND THE EULER-MARUYAMA METHOD
    Li, Guangjie
    Yang, Qigui
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (03): : 1259 - 1272
  • [44] An adaptive weak continuous Euler-Maruyama method for stochastic delay differential equations
    B. Akhtari
    E. Babolian
    A. Foroush Bastani
    Numerical Algorithms, 2015, 69 : 29 - 57
  • [45] EQUIVALENCE OF STABILITY AMONG STOCHASTIC DIFFERENTIAL EQUATIONS, STOCHASTIC DIFFERENTIAL DELAY EQUATIONS, AND THEIR CORRESPONDING EULER-MARUYAMA METHODS
    Zhang, Yuhang
    Song, Minghui
    Liu, Mingzhu
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (09): : 4761 - 4779
  • [46] Almost Sure Exponential Stability of Stochastic Differential Delay Equations
    Zhang, Wei
    Song, M. H.
    Liu, M. Z.
    FILOMAT, 2019, 33 (03) : 789 - 814
  • [47] ALMOST SURE EXPONENTIAL STABILITY OF STOCHASTIC DIFFERENTIAL DELAY EQUATIONS
    Guo, Qian
    Mao, Xuerong
    Yue, Rongxian
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (04) : 1919 - 1933
  • [48] Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations
    MENG Xuejing
    LYU Linfeng
    Wuhan University Journal of Natural Sciences, 2023, 28 (05) : 399 - 410
  • [49] Stability in the small moment sense of the backward Euler-Maruyama method for stochastic differential equations with sup er-linear coefficients
    Li, Xiaotong
    Liu, Wei
    Wang, Yudong
    Wu, Ruoxue
    APPLIED MATHEMATICS LETTERS, 2023, 139
  • [50] On exponential stability of non-autonomous stochastic differential equations with Markovian switching
    Tran, Ky Q.
    Le, Bich T. N.
    STATISTICS & PROBABILITY LETTERS, 2022, 189
12345