求解随机微分方程半隐无导数法的稳定性

Mean square stability and exponential stability of the semi-implicit derivative-free methods for solving stochastic differential equations

数值方法的有效性对于求解随机微分方程是很重要的,稳定性就是衡量其合理性的标准之一.讨论了在噪声为乘性噪声的条件下,半隐无导数法用于求解标量自治随机微分方程的均方稳定性和指数稳定性,并给出了半隐无导数法用于求解标量自治随机微分方程的均方稳定性和指数稳定性的条件,同时指出半隐无导数法用于求解标量自治随机微分方程的均方稳定性和指数稳定性是等价的.

The validity of numerical method to be solved stochastic differential equation is very important, and the stability is one of the criteria used to judge its rationality. When noise is multiplicative noise, semi-implicit derivative-free method is used to solve scalar autonomous stochastic differential equations is explored and their mean-square stability and exponential stability are found in this paper. The condition of mean-square stability and exponential stability is put forward under which semi-implicit derivative-free method be used to solve scalar autonomous stochastic differential equations, when semi-implicit derive- ative -free method is used to solve scalar autonomous stochastic differential equations, at the same time, it is pointed out that mean-square stability is equivalent to exponential stability.