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带有Poisson跳的随机延迟微分方程数值算法的几乎必然指数稳定性

Almost Sure Exponential Stability of Stochastic Delay Differential Equations with Poisson Jumps
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摘要 运用Lyapunov函数和半鞅收敛定理,研究了带有Poisson跳的随机延迟微分方程(SDDEJ)在满足局部Lipschitz条件和线性增长条件时,如何保证全局解的唯一存在性,证明了用EM算法和倒向EM算法求解带有Poisson跳的随机延迟微分方程(SDDEJ)所得数值解的几乎必然指数稳定性. By using Lyapunov function and semimartingale convergence theorems, this paper investigateshow to guarantee the unique existence of the global solution when the stochastic delay differential equations withPoisson jumps （SDDEJ） satisfy- the local Lipschitz condition and the linear growth condition. The almost sure ex-ponential stability of the numerical solutions by EM method and backward EM method for the SDDEJs areproved.
作者 袁玲 唐江花 梁静 YUAN Ling;TANG Jianghua;LIANG Jing(Department of Liberal Education,Anhui Xinhua University,Hefei,Anhui 230088,China)
机构地区 安徽新华学院通识教育部
出处 《平顶山学院学报》 2018年第5期24-31,共8页 Journal of Pingdingshan University
基金 安徽新华学院科研项目(2016zr011) 安徽省重点科研项目(KJ2017A623)
关键词 带有Poisson跳的随机延迟微分方程 EM算法 倒向EM算法 几乎必然指数稳定性 Stochastic delay differential equations with Poisson jumps EM method backward EM method almmost sure exponential stability
分类号 O241.8 [理学—计算数学]
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平顶山学院学报
2018年 第5期

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