| 具有Markov调制的随机种群系统半驯服Euler法的指数稳定性 |
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| 引用本文： | 杨洪福,张启敏.具有Markov调制的随机种群系统半驯服Euler法的指数稳定性[J].数学年刊A辑(中文版),2016,37(1):71-88. |
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| 作者姓名： | 杨洪福 张启敏 |
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| 作者单位： | 北方民族大学数学与信息科学学院, 银川 750021.,通讯作者.北方民族大学数学与信息科学学院, 银川 750021. |
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| 基金项目： | 本文受到国家自然科学基金(No.11461053,No.11261043)的资助 |
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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、It\^{o} 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.
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| 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 |
| 收稿时间： | 5/5/2014 12:00:00 AM |
| 修稿时间： | 5/4/2015 12:00:00 AM |
Exponential Stability of the Semi-tamed Euler Scheme for the Stochastic Age-Dependent Population System with Markov Switching |
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| YANG Hongfu and ZHANG Qimin.Exponential Stability of the Semi-tamed Euler Scheme for the Stochastic Age-Dependent Population System with Markov Switching[J].Chinese Annals of Mathematics,2016,37(1):71-88. |
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| Authors: | YANG Hongfu and ZHANG Qimin |
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| Institution: | School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China. and Corresponding author. School of Mathematics and Information Science, Beifang University of
Nationalities, Yinchuan 750021, China. |
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| Abstract: | 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, It\^{o} 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. |
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| Keywords: | Stochastic age-dependent population system Mean square stability Semi-tamed Euler scheme Non-local Lipschitz condition Markov chain |
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