论文标题
EULER方案的强大收敛速率具有不规则漂移，由征费噪声驱动
Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise
论文作者
论文摘要
我们研究了Euler-Maruyama方案的强大收敛速度，用于多维随机微分方程（SDE）$$ dx_t = b（x_t）\，dt + dl_t，$ dl_t，与不规则$β$-HöldEll，$β$β> 0 $ driven $β> $β> 0 $ contrance $ bys $ $ $ bytem $ $ bys $ bytemant $ bytement（0） $α\在[2/3，2] $中，我们获得了强大的$ l_p $，并且在整个范围内收敛速度$β> 1 -α/2 $，其中已知SDE的范围很大，这显着地提高了当前的艺术品状态。平滑的漂移是无关的，我们表明，这种SDE的欧拉山的方案几乎可以融合，并获得明确的收敛速度。争论和Lê的定量约翰·尼伦贝格不平等。
We study the strong rate of convergence of the Euler--Maruyama scheme for a multidimensional stochastic differential equation (SDE) $$ dX_t = b(X_t) \, dt + dL_t, $$ with irregular $β$-Hölder drift, $β> 0$, driven by a Lévy process with exponent $α\in (0, 2]$. For $α\in [2/3, 2]$, we obtain strong $L_p$ and almost sure convergence rates in the entire range $β> 1 - α/2$, where the SDE is known to be strongly well-posed. This significantly improves the current state of the art, both in terms of convergence rate and the range of $α$. Notably, the obtained convergence rate does not depend on $p$, which is a novelty even in the case of smooth drifts. As a corollary of the obtained moment-independent error rate, we show that the Euler--Maruyama scheme for such SDEs converges almost surely and obtain an explicit convergence rate. Additionally, as a byproduct of our results, we derive strong $L_p$ convergence rates for approximations of nonsmooth additive functionals of a Lévy process. Our technique is based on a new extension of stochastic sewing arguments and Lê's quantitative John-Nirenberg inequality.
