Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
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非全局Lipschitz连续系数交换随机微分方程半驯服Milstein法的收敛性和稳定性
DOI：
10.1016/j.amc.2021.126680
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发表时间：
2021-10
影响因子：
4
通讯作者：
Xiujun Cheng
中科院分区：
文献类型：
--
作者：
Yulong Liu;Yuanling Niu;Xiujun Cheng
针对具有非全局Lipschitz连续系数的可交换随机微分方程，提出了一种新的1阶显式随机格式。该方法是求解漂移系数由非Lipschitz连续项和全局Lipschitz连续项组成的SDEs的Milstein格式的半简化版。该方法易于实现，且具有较高的强收敛阶。导出了该方法的稳定性判据，表明数值方法的稳定性条件与解方程的稳定性条件保持一致。与一些常用的数值格式相比，该方法在继承SDEs精确解的均方稳定性方面具有更好的性能。数值实验证明了所得到的收敛性和稳定性。
A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to solve SDEs with the drift coefficient consisting of non-Lipschitz continuous term and globally Lipschitz continuous term. It is easily implementable and achieves higher strong convergence order. A stability criterion for this method is derived, which shows that the stability condition of the numerical methods and that of the solved equations keep uniform. Compared with some widely used numerical schemes, the proposed method has better performance in inheriting the mean square stability of the exact solution of SDEs. Numerical experiments are given to illustrate the obtained convergence and stability properties.
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DOI：
--
发表时间：
2009-05
期刊：
--
影响因子：
--
作者：
Martin Hutzenthaler;Arnulf Jentzen
通讯作者：
Martin Hutzenthaler;Arnulf Jentzen
DOI：
10.1080/17442509408833885
发表时间：
1994-03
期刊：
Stochastics and Stochastics Reports
影响因子：
--
作者：
D. Talay
通讯作者：
D. Talay
影响因子：
3
作者：
Martin Hutzenthaler;Arnulf Jentzen
通讯作者：
Martin Hutzenthaler;Arnulf Jentzen
DOI：
--
发表时间：
1997
期刊：
Langmuir : the ACS journal of surfaces and colloids
影响因子：
--
作者：
X. Mao
通讯作者：
X. Mao
影响因子：
1.1
作者：
Gyongy, I
通讯作者：
Gyongy, I