| 随机时滞微分方程的随机线性θ方法的均方指数稳定性 |
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| 引用本文： | 赵梅,兰光强.随机时滞微分方程的随机线性θ方法的均方指数稳定性[J].北京化工大学学报(自然科学版),2019,46(5):118-122. |
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| 作者姓名： | 赵梅 兰光强 |
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| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
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| 基金项目： | 国家自然科学基金（11601025）；北京市自然科学基金（1192013） |
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| 摘 要： | 给出了随机时滞微分方程随机线性θ方法的均方指数稳定性的充分条件，证明了当扩散系数高度非线性（即不满足线性增长条件）时，随机线性θ方法仍可能均方指数稳定。本文研究结果在相同条件下加强了Huang在文献5]中关于随机线性θ方法稳定性的结果。
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| 关 键 词： | 随机时滞微分方程 随机线性θ方法 均方指数稳定性 |
| 收稿时间： | 2019-05-21 |
Mean square exponential stability of the stochastic linear theta method for stochastic delay differential equations |
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| ZHAO Mei,LAN GuangQiang.Mean square exponential stability of the stochastic linear theta method for stochastic delay differential equations[J].Journal of Beijing University of Chemical Technology,2019,46(5):118-122. |
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| Authors: | ZHAO Mei LAN GuangQiang |
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| Institution: | Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | In this work, the sufficient conditions for the mean square exponential stability of stochastic linear theta methods for stochastic delay differential equations are given. It is proved that when the diffusion coefficient is highly nonlinear (that is, it does not satisfy the linear growth condition), the stochastic linear theta method still has mean square exponential stability. Finally, the results of a previous paper by Huang (Journal of Computational and Applied Mathematics, 2014, 259:77-86) are strengthened under the same conditions. |
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| Keywords: | stochastic delay differential equations stochastic linear θ method" target="_blank">θ method')">stochastic linear θ method mean square exponential stability |
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