随机微分方程波形松弛方法的稳定性

The stability of waveform relaxation methods for stochastic differential equations

针对随机微分方程,提出波形松弛方法的稳定性定义,给出了方法稳定的充分条件,证明了方法在给定的条件下是渐进均方稳定的。将得到的定理用于线性随机微分方程,获得了方法的稳定性条件,该条件表明:对应特定分裂函数的波形松弛方法是稳定的。

The stability of waveform relaxation methods of stochastic differential equations was de- fined with the efficient conditions of the stability. The waveform relaxation methods were proved to be asymptotically mean squared stable under the given conditions. The stable conditions of the linear stochastic differential equations were obtained using the derived theorem. The results show that the waveform relaxation methods are stable for some specifically splitting functions.