This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical $\alpha$-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as $\alpha \to 2$. Also, the rate of weak convergence, which depends on $2-\alpha$, for the solution towards the solution of the limit equation is obtained. For illustration, the results are applied to a simple one-dimensional stochastic differential equation, which implies the rate of weak convergence is optimal.

中文翻译：

---

圆柱非对称α-稳定Lévy过程驱动的随机微分方程的极限分布

本文研究由非对称圆柱驱动的随机微分方程的极限分布$\alpha$- 稳定的过程。在适当的条件下，证明该方程的解弱收敛于 Skorohod 空间中由布朗运动驱动的随机微分方程的解：$\alpha \to 2$。此外，弱收敛速度取决于$2-\alpha$，获得极限方程解的解。为了便于说明，将结果应用于简单的一维随机微分方程，这意味着弱收敛速度是最优的。