二阶线性随机微分方程的渐近稳定性

On the Asymptotic Stability of Second order Linear Stochastic Equation

对刚度系数是遍历过程的二阶线性随机微分方程，本文研究了其平凡解几乎处处渐近稳定性问题。利用刚度系数导数过程的性质，给出了平凡解几乎处处渐近稳定的充分条件。当刚度系数是遍历高斯过程或周期过程时，还具体计算了其渐进稳定区域。结果表明，本文结果改进了目前有关的渐近稳定性的条件。

In this paper we present a study of the almost sure asymptotic stability properties of second order linear stochastic system with an egodic stiffness coefficient. Using the probabilistic property of the derivative process of the stiffness coefficient, we obtain the stability condilions and present the numerical results for the cases of a Gaussian noise coefficient and periodic coefficient. The results are found to be an improvement over priviously available results for stochastic systems with slochastic stiffness.