Wasserstein convergence rates for random bit approximations of continuous Markov processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:493

Article

Ankirchner, Stefan¹  Kruse, Thomas²  Urusov, Mikhail³ 

[1] Univ Jena, Inst Math, Ernst Abbe Pl 2, D-07745 Jena, Germany

[2] Univ Giessen, Inst Math, Arndtstr 2, D-35392 Giessen, Germany

[3] Univ Duisburg Essen, Fac Math, Thea Leymann Str 9, D-45127 Essen, Germany

关键词: One-dimensional Markov process;    Speed measure;    Markov chain approximation;    Numerical scheme;    Rate of convergence;    Wasserstein distance;   

DOI  :  10.1016/j.jmaa.2020.124543

来源: Elsevier

【 摘 要 】

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 certain 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free