| 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,2016,37(1):71~88 |
| 具有Markov调制的随机种群系统半驯服Euler法的指数稳定性 |
| Exponential Stability of the Semi-tamed Euler Scheme for the Stochastic Age-Dependent Population System with Markov Switching |
| Received:May 05, 2014 Revised:May 04, 2015 |
| DOI： |
| 中文关键词: 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 |
| 英文关键词:Stochastic age-dependent population system, Mean square stability,
Semi-tamed Euler scheme, Non-local Lipschitz condition, Markov chain |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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