We determine the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes. The scheme is based on the construction of coin tossing Markov chains whose laws can be embedded into the process with a sequence of stopping times. Under a mild condition on the process' speed measure we prove that the approximating Markov chains converge at fixed times at the rate of $1/4$ with respect to every $p$-th Wasserstein distance. For the convergence of paths, we prove any rate strictly smaller than $1/4$. Our results apply, in particular, to processes with irregular behavior such as solutions of SDEs with irregular coefficients and processes with sticky points.

中文翻译：

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连续马尔可夫过程的随机位近似的 Wasserstein 收敛率

我们确定近似一维连续强马尔可夫过程的数值方案的收敛速度。该方案基于抛硬币马尔可夫链的构建，其定律可以嵌入到具有一系列停止时间的过程中。在过程速度度量的温和条件下，我们证明了近似马尔可夫链在固定时间以 $1/4$ 的速率收敛于每个 $p$-th Wasserstein 距离。对于路径的收敛，我们证明任何速率都严格小于 $1/4$。我们的结果特别适用于具有不规则行为的过程，例如具有不规则系数的 SDE 解和具有粘性点的过程。