Uniqueness of a three-dimensional stochastic differential equation

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.

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