Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
It provides a convergence guarantee for a class of SDEs where standard theory fails, benefiting researchers in numerical analysis and stochastic modeling.
The paper proves strong convergence of order 1/4-ε for the Euler-Maruyama method applied to multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient.
We prove strong convergence of order $1/4-ε$ for arbitrarily small $ε>0$ 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.