论文标题
随机米尔斯坦算法，用于近似跳跃SDE的溶液
Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs
论文作者
论文摘要
我们研究了用于求解标量跳跃随机微分方程的随机米尔斯坦算法的误差。我们在基本上弱的假设下提供了完全误差分析，该假设比文献中所知。如果满足了跳跃交换性条件，我们通过证明匹配的下限来证明随机米尔斯坦算法的最佳性。此外，我们通过研究了lévyslévys区域的近似值的最佳收敛速率，从而对多维案例进行了深入了解。最后，我们报告了支持我们理论发现的数值实验。
We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than known in the literature. In case the jump-commutativity condition is satisfied, we prove optimality of the randomized Milstein algorithm by proving a matching lower bound. Moreover, we give some insight into the multidimensional case by investigating the optimal convergence rate for the approximation of jump-diffusion type Lévys' areas. Finally, we report numerical experiments that support our theoretical findings.
