We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the stability index $\alpha$ lies in the range $(1,2)$, and the drift term exhibits anisotropic $\beta$-H\"older continuity with $\beta >1 - \frac{\alpha}{2}$. We establish a convergence rate of $(\frac{1}{2} + \frac{\beta}{\alpha(1+\alpha)} \wedge \frac{1}{2})$, which aligns with the results in [4] concerning first-order SDEs.

翻译：我们研究了一类由α稳定过程驱动的奇异随机动力学方程（亦称为二阶随机微分方程）解的强逼近问题，采用了一种受文献[11]启发的欧拉型数值格式。对于此类方程，其稳定性指数α位于区间(1,2)内，且漂移项具有各向异性的β-Hölder连续性，其中β > 1 - α/2。我们证明了数值格式的收敛速度为(1/2 + β/(α(1+α)) ∧ 1/2)，该结果与文献[4]中关于一阶随机微分方程的结论相一致。