论文标题
具有不连续漂移系数的跳转SDE的高阶近似方法
A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
论文作者
论文摘要
我们介绍了与不连续漂移的跳跃随机微分方程解的第一个高阶近似方案。对于此基于转换的跳跃化准米尔斯坦方案，我们证明了$ l^p $ -Convergence订单3/4。为了获得这一结果，我们证明，在稍强的假设（但仍然比以前更弱），相关的跳跃准米尔斯坦方案的相关假设方案的收敛顺序为3/4-在特殊情况下甚至是1。
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.
