AI 中文总结
研究具有奇异漂移、乘性布朗及列维噪声的多维随机微分方程的驯服欧拉格式，基于非局部Zvonkin变换等方法，通过误差分解得出强收敛率，能分离跳跃贡献，在跳跃系数消失时恢复布朗型估计。
AI 中文摘要
我们证明了具有奇异漂移、乘性布朗噪声和乘性列维噪声的多维随机微分方程的驯服欧拉格式的强收敛率。假设漂移满足Ladyzhenskaya - Prodi - Serrin型条件，扩散和跳跃系数具有Sobolev型空间正则性。证明基于非局部Zvonkin变换、Krylov型估计和随机Gronwall论证。主要新颖之处在于误差分解，分离出两个跳跃引起的贡献：补偿跳跃鞅误差和由欧拉冻结引起的非局部补偿误差。这种分解产生显式速率，并在跳跃系数消失时恢复布朗型估计。
英文摘要
We prove strong convergence rates for tamed Euler schemes of multidimensional stochastic differential equations with singular drift, multiplicative Brownian noise, and multiplicative Levy noise. The drift is assumed to satisfy a Ladyzhenskaya-Prodi-Serrin type condition, while the diffusion and jump coefficients have Sobolev-type spatial regularity. The proof is based on a nonlocal Zvonkin transform, Krylov-type estimates, and a stochastic Gronwall argument. The main novelty is an error decomposition that isolates two jump-induced contributions: a compensated jump martingale error and a nonlocal compensator error caused by Euler freezing. This decomposition yields explicit rates and recovers the Brownian-type estimate when the jump coefficient vanishes.
