Wasserstein convergence rates for random bit approximations of\n continuous Markov processes

We determine the convergence speed of a numerical scheme for approximating\none-dimensional continuous strong Markov processes. The scheme is based on the\nconstruction of coin tossing Markov chains whose laws can be embedded into the\nprocess with a sequence of stopping times. Under a mild condition on the\nprocess' speed measure we prove that the approximating Markov chains converge\nat fixed times at the rate of $1/4$ with respect to every $p$-th Wasserstein\ndistance. For the convergence of paths, we prove any rate strictly smaller than\n$1/4$. Our results apply, in particular, to processes with irregular behavior\nsuch as solutions of SDEs with irregular coefficients and processes with sticky\npoints.\n