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：在本文中，我们证明了数值方法在具有不连续漂移项的跳跃扩散随机微分方程（SDEs）中的尖锐误差下界。我们研究了使用非自适应以及跳跃自适应逼近方案的跳跃扩散SDE的逼近，并为两类逼近方案提供了$3/4$阶的误差下界。这导致了基于变换的跳跃自适应拟米尔斯坦方案的最优性。