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A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient

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Abstract

It is shown that the Euler–Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic differential equation with the same initial condition. The proof uses upper and lower solutions of the stochastic differential equations and the Euler–Maruyama scheme.

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Authors and Affiliations

  1. Department of Statistics and Actuarial-Finance Mathematics, University of the Aegean, Karlovassi, 83200, Samos, Greece

    Nikolaos Halidias

  2. Institut für Mathematik, Johann Wolfgang Goethe Universität, 60054, Frankfurt am Main, Germany

    Peter E. Kloeden

Authors
  1. Nikolaos Halidias
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  2. Peter E. Kloeden
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Correspondence to Peter E. Kloeden.

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AMS subject classification (2000)

60H10, 60H20, 60H30

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Halidias, N., Kloeden, P. A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient . Bit Numer Math 48, 51–59 (2008). https://doi.org/10.1007/s10543-008-0164-1

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  • DOI: https://doi.org/10.1007/s10543-008-0164-1

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