In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes and provide lower error bounds of order $3/4$ for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

翻译：本文证明了带间断漂移项的跳跃扩散随机微分方程（SDEs）数值方法的精确下界误差估计。我们研究了非自适应及跳跃自适应两种近似方案对跳跃扩散SDE的近似问题，并给出了两类方案均为$3/4$阶的下界误差。这证明了基于变换的跳跃自适应拟Milstein方案的最优性。