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

Abstract

We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon >0$ 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.

References in corpus (7)

• A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift
• Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
• A Numerical Method for SDEs with Discontinuous Drift
• On stochastic differential equations with arbitrary slow convergence rates for strong approximation
• On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients
• Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information
• On hard quadrature problems for marginal distributions of SDEs with bounded smooth coefficients

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