arXiv:2610.28243v1 Announce Type: new Abstract: While well-established approaches exist for computing probability densities of stochastic differential equations driven by Brownian motion, computing probability densities for general stochastic differential equations driven by {\alpha}-stable processes remains challenging, and few general-purpose methods are available. A major difficulty is that the corresponding Fokker--Planck equations governing the density are generally unavailable in explicit form. In this paper, we develop an efficient approach to compute probability densities for stochastic differential equations driven by {\alpha}-stable processes without relying on Fokker--Planck equations or any other governing equations. The proposed approach is easy to implement and computationally efficient. Numerical examples demonstrate its effectiveness and indicate an approximately first-order convergence rate with respect to the time step.