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Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient (2206.00088v1)
Published 10 May 2022 in math.PR, cs.NA, and math.NA
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.