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 for arbitrarily small 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}
}