Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient

Huimin Hu; Siqing Gan

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arXiv · 2206.00088

Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient

Huimin Hu·Siqing Gan

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Abstract

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the classical $L_p$-error rate 1/2 for all $p\in [1, +\infty)$ is recovered for the tamed Euler scheme. A numerical example is provided to support our conclusion.

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BibTeX RIS

Huimin Hu, Siqing Gan. 2022-05-10. Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient. https://arxiv.org/abs/2206.00088

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