论文标题
三维随机微分方程的唯一性
Uniqueness of a three-dimensional stochastic differential equation
论文作者
论文摘要
In order to extend the study of uniqueness property of multi-dimensional systems of stochastic differential equations, in this paper, we look at the following three-dimensional system of equations, of which the two-dimensional case was well-studied before: $dX_t=Y_tdt\quad, dY_t=Z_tdt,\quad dZ_t=|X_t|^αdB_t$.我们证明，如果$（x_0，y_0，z_0）\ neq（0,0,0）$和$ \ frac {3} {4} {4} <α<1 $，那么方程式系统在强大的意义上具有独特的解决方案。
In order to extend the study of uniqueness property of multi-dimensional systems of stochastic differential equations, in this paper, we look at the following three-dimensional system of equations, of which the two-dimensional case was well-studied before: $dX_t=Y_tdt\quad, dY_t=Z_tdt,\quad dZ_t=|X_t|^αdB_t$. We proved that if $(X_0,Y_0,Z_0)\neq(0,0,0)$, and $\frac{3}{4}<α<1$, then the system of equations has a unique solution in the strong sense.
