1. A note on the asymptotic stability of the Semi-Discrete method for Stochastic Differential Equations
- Author
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Halidias, Nikolaos and Stamatiou, Ioannis S.
- Subjects
Mathematics - Numerical Analysis ,60H10, 60H35, 65C20, 65C30, 65J15, 65L20 - Abstract
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed that it can be arbitrarily close to $1/2,$ see \textit{Stamatiou, Halidias (2019), Convergence rates of the Semi-Discrete method for stochastic differential equations, Theory of Stochastic Processes, 24(40)}. We show that the truncated SD method is able to preserve the asymptotic stability of the underlying SDE. Motivated by a numerical example, we also propose a different SD scheme, using the Lamperti transformation to the original SDE, which we call Lamperti semi-discrete (LSD). Numerical simulations support our theoretical findings., Comment: 18 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2001.07483
- Published
- 2020