关于随机微分方程组整体解存在性的一点注记

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

本文在将 Schrdinger 波函数角变量参数化后,利用随机力学与扩散过程的关系,得出了一族稳态扩散过程轨道状态守恒律,讨论了随机微分方程组的整体解.

In this paper,we first get a stochastic Newton equation m[1/2(D+D_-+D_-D_+)x_t+1/8β(D^+-D_-)~2x_t]=-grad_xV((X_9ts)t) (1) and a pathwise oonservation law for stationary diffusion processes with a parameter μ m[μ~2/2|▽f(x_t)|~2+μ~2/2Δf(x_t)]+(x_t)=E(x_0_ (2) Second,we disouss a global solution of the stohastic differential equation dx_t=μ▽f(x_t)dt+dw_t,x_0=η (3)