A numerical method for SDEs with discontinuous drift

By Gunther Leobacher, Michaela Szolgyenyi. BIT Numerical Mathematics, 2015

62 citations recorded by the source corpus.

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/2$$\end{document}. Finally, we present numerical examples.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c4030f4d55156a2cae67d45c4b52613e28f96e74

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Citations in the corpus

On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients (2015, background): “[21] Leobacher, G. and Szölgyenyi M.: A numerical method for SDEs with discontinuous drift.”
On the performance of the Euler–Maruyama scheme for SDEs with discontinuous drift coefficient (2018, methodology): “We add that in [14, 15] a numerical method for approximating X1 is constructed that is based on a suitable transformation of the solution X of (1) and achieves an L2-error rate of at”