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- W4287691943 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." @default.
- W4287691943 created "2022-07-26" @default.
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- W4287691943 date "2020-08-06" @default.
- W4287691943 modified "2023-09-23" @default.
- W4287691943 title "A note on the asymptotic stability of the Semi-Discrete method for Stochastic Differential Equations" @default.
- W4287691943 doi "https://doi.org/10.48550/arxiv.2008.03148" @default.
- W4287691943 hasPublicationYear "2020" @default.
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