A Numerical Method for SDEs with Discontinuous Drift

Abstract

In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient. One the other hand we present a numerical method based on transforming the Euler-Maruyama scheme for such a class of SDEs. We prove convergence of order $1/2$. Finally, we present numerical examples.

References in corpus (1)

• On the Existence of Solutions of a Class of SDEs with Discontinuous Drift and Singular Diffusion

Cited by in corpus (19)

• 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
• An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis
• On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
• The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence Rates via Reduction to a Quadrature Problem
• Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information
• Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps
• Numerical solutions of Fokker-Planck equations with drift-admitting jumps
• Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift
• Convergence rate of EM algorithm for SDEs under integrability condition
• The Euler scheme for stochastic differential equations with discontinuous drift coefficient: A numerical study of the convergence rate
• Dividend maximization in a hidden Markov switching model
• A generalized Avikainen's estimate and its applications
• Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient
• Weak convergence of Euler scheme for SDEs with singular drift
• On mixed fractional SDEs with discontinuous drift coefficient
• Bicausal optimal transport for SDEs with irregular coefficients
• Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms
• Estimate of Heat Kernel for Euler-Maruyama Scheme of SDEs Driven by α-Stable Noise and Applications