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

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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1809.08423, arXiv:2204.02343 by other authors