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

2019/03/19 by Stefan Ankirchner, Thomas Kruse, Ankirchner, Stefan +3
Mathematics · #60H35 #60J22 #60J25 #60J60 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.07880

openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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\n1/4. Our results apply, in particular, to processes with irregular behavior\nsuch as solutions of SDEs with irregular coefficients and processes with sticky\npoints.\n

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