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On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric $α$-stable Lévy processes
Ting Li, Hongbo Fu, Xianming Liu · 2023-02-17 · via math.PR updates on arXiv.org

This article deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical $α$-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 $α\rightarrow2$. Also, the rate of weak convergence, which depends on $ 2-α$, 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.

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