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An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis

by A. Neuenkirch and M. Szölgyenyi and L. Szpruch

(Report number 2018-06)

Abstract
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an adaptive step sizing strategy for the explicit Euler-Maruyama scheme. As a result, we obtain a numerical method which has - up to logarithmic terms - strong convergence order (1/2) with respect to the average computational cost. We support our theoretical findings with several numerical examples.

Keywords: stochastic differential equations, discontinuous drift, degenerate diffusion, adaptive Euler-Maruyama scheme, strong convergence order

@Techreport{NSS18_760,
  author = {A. Neuenkirch and M. Sz\"olgyenyi and L. Szpruch},
  title = {An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-06.pdf },
  year = {2018}
}

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