摘要
随机微分方程广泛地出现于经济学、生物学、物理学、电子、无线电通讯等领域,所以研究随机微分方程的解是十分必要的.由于随机微分方程的解析解求解困难,其数值方法的研究越来越引起人们的重视.对于求解随机微分方程的数值方法,衡量其有效性的标准是收敛性和稳定性.本文证明混合欧拉格式用于求解自治标量随机微分方程时,在方程的偏移系数和扩散系数均满足线性增长条件和全局Lipschitz条件时的收敛性,并且求出了局部均值收敛阶和均方强收敛阶.接着讨论了两种试验方程混合欧拉格式的稳定性.
Stochastic differential equation has been widely used in economics, biology, physics, electronics, wireless communication, etc, it is very important to study its solution. Since most stochastic differential equations are not explicitly solvable, numerical analysis has aroused a lot of attention. In designing numerical schemes for solving stochastic differential equations, convergence and stability are the criteria to measure the efficiency of a numerical scheme. In this paper, it is proved that the composite Euler method is convergent when it is used to solve the scalar autonomous stochastic differential equations, where both the drift coefficient and the diffusion coefficient satisfy the linear growth condition and the global Lipschitz condition. The local convergence order and the mean square strong convergence order are presented as well. The stability condition of the composite Euler schemes of the test equation is discussed.
出处
《工程数学学报》
CSCD
北大核心
2013年第3期427-432,共6页
Chinese Journal of Engineering Mathematics
关键词
随机微分方程
混合欧拉法
收敛性
稳定性
stochastic differential equations
composite Euler method
convergence
stability
