On the averaging principle for stochastic delay differential equations with jumps

被引：0
|
作者：
Wei Mao
Surong You
Xiaoqian Wu
Xuerong Mao
机构：
[1] Jiangsu Second Normal University,School of Mathematics and Information Technology
[2] Donghua University,Department of Applied Mathematics
[3] University of Strathclyde,Department of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2015卷
关键词：
averaging principle; stochastic delay differential equations; Poisson random measure; convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate the averaging principle for stochastic delay differential equations (SDDEs) and SDDEs with pure jumps. By the Itô formula, the Taylor formula, and the Burkholder-Davis-Gundy inequality, we show that the solution of the averaged SDDEs converges to that of the standard SDDEs in the sense of pth moment and also in probability. Finally, two examples are provided to illustrate the theory.
引用
收藏
相关论文
共 50 条
  • [1] On the averaging principle for stochastic delay differential equations with jumps
    Mao, Wei
    You, Surong
    Wu, Xiaoqian
    Mao, Xuerong
    ADVANCES IN DIFFERENCE EQUATIONS, 2015,
  • [2] Averaging Principle for ?-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps
    Yang, Dandan
    Wang, Jingfeng
    Bai, Chuanzhi
    SYMMETRY-BASEL, 2023, 15 (07):
  • [3] The averaging principle of Hilfer fractional stochastic delay differential equations with Poisson jumps
    Ahmed, Hamdy M.
    Zhu, Quanxin
    APPLIED MATHEMATICS LETTERS, 2021, 112 (112)
  • [4] Weak order in averaging principle for stochastic differential equations with jumps
    Zhang, Bengong
    Fu, Hongbo
    Wan, Li
    Liu, Jicheng
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [5] Weak order in averaging principle for stochastic differential equations with jumps
    Bengong Zhang
    Hongbo Fu
    Li Wan
    Jicheng Liu
    Advances in Difference Equations, 2018
  • [6] The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps
    Bai, Zhenyu
    Bai, Chuanzhi
    AXIOMS, 2024, 13 (01)
  • [7] Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses
    Wang, Peiguang
    Xu, Yan
    COMPLEXITY, 2020, 2020
  • [8] An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion
    Xu, Yong
    Pei, Bin
    Li, Yongge
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [9] Stochastic Averaging Principle for Mixed Stochastic Differential Equations
    Jing Yuanyuan
    Peng Yarong
    Li Zhi
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2022, 35 (03): : 223 - 239
  • [10] Averaging Principle for Backward Stochastic Differential Equations
    Jing, Yuanyuan
    Li, Zhi
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2021, 2021
12345