一类泛函微分方程的随机压制

主要探讨布朗噪声对一类满足一般多项式增长条件的确定性泛函微分方程爆炸解的随机压制问题。对一类满足一般多项式增长条件的可能在有限时刻内出现爆炸解的确定性泛函微分方程，主要引入了一个多项式布朗噪声，使其对应的随机摄动泛函微分方程存在唯一的全局解，且应用Lyapunov方法研究得到了其全局解矩有界、随机一致有界、最多以多项式形式增长的结论。

Stochastic Suppression of a Class of Functional Differential Equations

The problem of stochastic suppression on the explosive solutions of nonlinear functional differential equations satisfying general polynomial growth condition was investigated by Brownian noise in this paper. For a class of deterministic functional differential equations satisfying general polynomial growth condition whose solutions may explode at a finite time, a polynomial Brownian noise was introduced to guarantee that there exists a unique global solution for the corresponding stochastically perturbed functional differential equation. By Lyapunov method, the fact is found that the global solution is bounded in the sense of the moment and the trajectory has large probability, and the global solution grows at most polynomial.