Wasserstein convergence rates for random bit approximations of continuous Markov processes
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1903.07880
- arXiv:
- arXiv:1903.07880
- Bibcode:
- 2019arXiv190307880A
- Keywords:
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- Mathematics - Probability;
- 60J22;
- 60J25;
- 60J60;
- 60H35
- E-Print:
- To appear in J. Math. Anal. Appl