In this article, we present a method to construct a positivity-preserving numerical scheme for a jump-extended CEV (Constant Elasticity of Variance) process, whose jumps are governed by a spectrally positive $\alpha$-stable process with $\alpha \in (1,2)$. The numerical scheme is obtained by making the diffusion coefficient $x^\gamma$, where $\gamma \in (\frac{1}{2},1)$, partially implicit and then finding the appropriate adjustment factor. We show that, for sufficiently small step size, the proposed scheme converges and theoretically achieves a strong convergence rate of at least $\frac{1}{2}\left(\frac{\alpha_-}{2} \wedge \frac{1}{\alpha}\wedge \rho\right)$, where $\rho \in (\frac{1}{2},1)$ is the H\"older exponent of the jump coefficient $x^\rho$ and the constant $\alpha_- < \alpha$ can be chosen arbitrarily close to $\alpha \in (1,2)$.

翻译：本文提出了一种构造正性保持数值格式的方法，用于跳跃扩展的CEV（常数弹性方差）过程，其跳跃由谱正$\alpha$-稳定过程（$\alpha \in (1,2)$）驱动。该数值格式通过将扩散系数$x^\gamma$（其中$\gamma \in (\frac{1}{2},1)$）部分隐式化，并寻找相应的调整因子而得到。我们证明，对于充分小的步长，所提格式收敛，理论上实现了至少$\frac{1}{2}\left(\frac{\alpha_-}{2} \wedge \frac{1}{\alpha}\wedge \rho\right)$的强收敛阶，其中$\rho \in (\frac{1}{2},1)$是跳跃系数$x^\rho$的赫尔德指数，常数$\alpha_- < \alpha$可任意接近$\alpha \in (1,2)$。