Multiscale schemes for stochastic dynamical systems driven by $α$-stable processes

Yanjie Zhang, Xiao Wang, Zibo Wang, Jinqiao Duan

Published 2020-04-22Version 1

This work is about strong and weak convergence of projective integration schemes for multiscale stochastic dynamical systems driven by $\alpha$-stable processes. Firstly, we analyze a class of "projective integration" methods, which are used to estimate the effect that the fast components have on slow ones. Secondly, we obtain the $p$th moment error bounds between the results of the projective integration method and the slow components of the original system with $p \in (1, \min(\alpha_1, \alpha_2))$. Finally, a numerical experiment is constructed to illustrate this scheme.