On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients

Abstract

We study the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is Hölder continuous. Especially, we show that the strong rate of the Euler-Maruyama approximation is 1/2 for a large class of equations whose drift is not continuous. We also provide the strong rate for equations whose drift is Hölder continuous and diffusion is nonconstant

23 pages

References in corpus (1)

• An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients

Cited by in corpus (5)

• Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
• The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence Rates via Reduction to a Quadrature Problem
• A numerical scheme for stochastic differential equations with distributional drift
• Convergence Rate of Euler-Maruyama Scheme for SDEs with Rough Coefficients
• Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient