English

Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

Numerical Analysis 2019-01-23 v7 Probability

Abstract

We prove strong convergence of order 1/4ϵ1/4-\epsilon for arbitrarily small ϵ>0\epsilon>0 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.

Keywords

Cite

@article{arxiv.1610.07047,
  title  = {Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient},
  author = {Gunther Leobacher and Michaela Szölgyenyi},
  journal= {arXiv preprint arXiv:1610.07047},
  year   = {2019}
}
R2 v1 2026-06-22T16:28:28.902Z