随机扰动下系统的稳定性问题

主要讨论了了无穷维空间中关于柱布朗运动的随机发展系统的稳定性问题，将Ｈｉｂｅｒｔ空间上的随机发展方程ｄＸｔ＝ＡＸｔｄｔ＋Ｇ（Ｘｔ）ｄＢｔ看作方程ｄＸｔ＝ＡＸｔｄｔ在随机扰动下的动力系统并讨论其解的稳定问题，即所谓的随机动下的系统稳定问题，主要结果有在加有限制的Ｇ（ｘ）的线性增长条件下，较直接得到其发展解的指数稳定性；利用一个积分不等式削弱关于Ｇ（ｘ）的线性增长条件，得到其Ｌ＾２－连续发展解的指数稳

On System Stability under Random Perturbations

In this paper we concider the problem of stability of stochastic evolution systemsin Hilbert space drived by a cylindrical Brownian mothin. We regard the stochestic evolutionequation dXt = AXtdt +G(Xt)dBt as a deterministic system of the form dXt=AXtdt under randomperturbation,and obtain stability of its solution. It is shown that under certain assumptions,itsevolution solution and L2-contimuous evulution solution are exponertially stable.