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In this paper, we first analyze the strong and weak convergence of projectiveintegration methods for multiscale stochastic dynamical systems driven by$\alpha$-stable processes, which are used to estimate the effect that the fastcomponents have on slow ones. Then we obtain the $p$th moment error boundsbetween the solution of slow component produced by projective integrationmethod and the solution of effective system with $p \in \left(1,\alpha\right)$. Finally, we corroborate our analytical results through aspecific numerical example.

Analysis of multiscale methods for stochastic dynamical systems driven by $\alpha$-stable processes