A REMARK ON THE EXISTENCE OF A GLOBAL SOLUTION OF THE STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,we first get a stochastic Newton equation m\left\frac12\left(D_+ D_-+D_- D_+\right) x_t+\frac18 \beta\left(D_+-D_-\right)^2 x_t\right=-\operatornamegrad_\alpha V\left(x_t, t\right) （1） and a pathwise oonservation law for stationary diffusion processes with a parameter μ m\left\frac\mu^22\left|\nabla f\left(x_t\right)\right|^2+\frac\mu^22 \Delta f\left(x_t\right)\right+\widetildeV\left(x_t\right)=E\left(x_0\right)（2） Second,we disouss a global solution of the stohastic differential equation d x_t=\mu \nabla f\left(x_t\right) d t+d w_t, \quad x_0=\eta（3）.