We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme we prove $L^p$-convergence order 3/4. To obtain this result, we prove that under slightly stronger assumptions (but still weaker than anything known before) a related jump-adapted quasi-Milstein scheme has convergence order 3/4 - in a special case even order 1. Order 3/4 is conjectured to be optimal.

翻译：摘要：本文提出了首个针对漂移不连续的跳扩散随机微分方程解的高阶逼近方案。对于这种基于变换的跳自适应拟Milstein方案，我们证明了其$L^p$-收敛阶为3/4。为获得这一结果，我们证明在稍强（但仍弱于此前已知条件）的假设下，相关跳自适应拟Milstein方案的收敛阶达到3/4——在特殊情况下甚至达到1阶。3/4阶被推测为最优收敛阶。