In this paper, by employing Gaussian type estimate of heat kernel, we establish Krylov's estimate and Khasminskill's estimate for EM algorithm. As applications, by taking Zvonkin's transformation into account, we investigate convergence rate of EM algorithm for a class of multidimensional SDEs under integrability conditions, where the drifts need not to be piecewise Lipschitz and are much more singular in some sense.

中文翻译：

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可积条件下SDE的EM算法收敛率

本文采用热核的高斯型估计，建立了EM算法的Krylov估计和Khasminskill估计。作为应用，通过考虑 Zvonkin 变换，我们研究了一类多维 SDE 在可积性条件下的 EM 算法的收敛速度，其中漂移不必是分段 Lipschitz 并且在某种意义上更加奇异。