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.