A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift

Abstract

In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method that converges with strong order 1/2. Our result is the first one that shows strong convergence for such a general class of SDEs. The proof is based on a transformation technique that removes the discontinuity from the drift such that the coefficients of the transformed SDE are Lipschitz continuous. Thus the Euler-Maruyama method can be applied to this transformed SDE. The approximation can be transformed back, giving an approximation to the solution of the original SDE. As an illustration, we apply our result to an SDE the drift of which has a discontinuity along the unit circle.

References in corpus (6)

• A Numerical Method for SDEs with Discontinuous Drift
• Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information
• On the Existence of Solutions of a Class of SDEs with Discontinuous Drift and Singular Diffusion
• Bayesian Dividend Optimization and Finite Time Ruin Probabilities
• Dividend maximization in a hidden Markov switching model
• Existence, Uniqueness and Regularity of the Projection onto Differentiable Manifolds

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