| Abstract: | In this talk, we shall investigate the strong and weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with low regularity drifts. For the strong convergence rate, by employing Gaussian type estimate of heat kernel, we establish Krylov's estimate and Khasminskii's estimate for EM algorithm. Explicit convergence rates are obtained by taking Zvonkin's transformation into account. The weak convergence rate is obtained by using Girsanov's transformation for EM algorithm. In both cases, drifts satisfy an integrability condition including discontinuous functions which can be non-piecewise continuous. |
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