标题： 强阶1的跳扩散SDEs不连续漂移自适应近似 显示英文标题

标题： Stong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift

摘要： 我们提出了一种自适应逼近方案，用于具有不连续漂移（以及可能退化扩散）的跳扩散随机微分方程（SDE）。 这种基于变换的双重自适应拟Milstein格式是首个对于这些SDE而言，在平均计算成本下强收敛率为$1$的格式，并且适用于$L^p$的情况$p\in[1,\infty)$。 为了得到我们的结果，我们证明了在比现有文献稍强但仍然较弱的假设下，一个相关的双重自适应拟Milstein格式具有收敛阶$1$。 该格式被称为双重自适应，因为它是一种跳跃适应型，即泊松噪声的所有跳跃时间都是网格点，并且它包含一种自适应步长策略以应对漂移的不连续性。 显示英文摘要

摘要： We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Milstein scheme is the first scheme that has strong convergence rate $1$ in $L^p$ for $p\in[1,\infty)$ with respect to the average computational cost for these SDEs. To obtain our result, we prove that under slightly stronger assumptions which are still weaker than those in existing literature, a related doubly-adaptive quasi-Milstein scheme has convergence order $1$. This scheme is doubly-adaptive in the sense that it is jump-adapted, i.e.~all jump times of the Poisson noise are grid points, and it includes an adaptive stepsize strategy to account for the discontinuities of the drift.