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arXiv · 2004.10580

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

Yanjie Zhang·Xiao Wang·Zibo Wang·Jinqiao Duan
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Abstract

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

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Yanjie Zhang, Xiao Wang, Zibo Wang, Jinqiao Duan. 2020-04-22. Analysis of multiscale methods for stochastic dynamical systems driven by $\alpha$-stable processes. https://arxiv.org/abs/2004.10580

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