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具有Markov调制的随机年龄结构种群系统半驯服Euler法的指数稳定性 被引量：2

Exponential Stability of the Semi-tamed Euler Scheme for the Stochastic Age-Dependent Population System with Markov Switching
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摘要 根据半驯服Euler法讨论了具有Markov调制的随机年龄结构种群系统的数值解.在非局部Lipschitz条件下,利用Burkholder-Davis-Gundy不等式、Ito公式和Gronwall引理,证明了半驯服Euler数值解不仅强收敛阶数为0.5,而且这种方法在时间步长一定的条件下有很好的均方指数稳定性.最后通过数值例子对所给的结论进行了验证. In this paper, the semi-tamed Euler scheme for the stochastic age-dependent population system with Markovian switching is discussed. Under the non-local Lipschitz condition, by using Burkholder-Davis-Gundy inequality, Ito formula and Gronwall lemma, it is shown that the semi-tamed Euler method converges strongly with the standard order one- half to the exact solution. The authors also reveal that the scheme does have an advantage in reproducing the mean square stability of the exact solution with fixed stepsizes. A numerical example is provided to illustrate the theoretical results.
作者 杨洪福 张启敏 YANG Hongfu ZHANG Qimin(School of Mathematics and Information Science, Beifang University of Nation- alities, Yinchuan 750021, China. 2Corresponding author. School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China.)
机构地区 北方民族大学数学与信息科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2016年第1期71-88,共18页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.11461053 No.11261043)的资助
关键词 随机年龄结构种群系统 均方稳定 半驯服Euler法 非局部Lipschitz条件 Markov链 Stochastic age-dependent population system, Mean square-sta-bility, Semi-tamed Euler scheme, Non-local Lipschitz condition,Markov chain
分类号 O211.63 [理学—概率论与数理统计] O175.21 [理学—基础数学]
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参考文献19

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二级参考文献43

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数学年刊（A辑）
2016年 第1期

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